Area of a Rectangle: Using variables

Rectangle ABCD has an area of

40 cm².

Side BC is equal to 5 cm.
Work out the value of x.

Let's multiply side AB by side BC

We'll set up the data as follows:

$5(2x+4)=40$

Let's multiply 5 by each term in parentheses:

$10x+20=40$

We'll move 20 to the right side and change its sign accordingly:

$10x=40-20$

Now we get:

$10x=20$

Let's divide both sides by 10:

$x=2$

2

The area of the rectangle below is equal to 50.

AC = 5

AB = 4X

Calculate X.

The area of the rectangle is equal to the length multiplied by the width.

Let's begin by presenting the known data:

$50=5\times4x$

$50=20x$

Let's finish by dividing both sides by 20:

$x=2.5$

2.5

The area of the rectangle below is equal to 28.

AC = 4

AB = X + 5

Calculate X.

The area of the rectangle is equal to the length multiplied by the width.

Let's present the known data:

$28=4\times(x+5)$

$28=4x+20$

We'll move 20 to the left side and maintain the appropriate sign:

$28-20=4x$

$8=4x$

Let's divide both sides by 4:

$x=2$

2

The area of the rectangle is equal to 27.

AC = 3

AB = 3X

Calculate X.

The area of a rectangle is equal to the length multiplied by the width.

Let's insert the known data into the formula:

$27=3\times3x$

$27=9x$

Lastly let's divide both sides by 9:

$x=3$

3

The area of the rectangle below is equal to 24.

AC = 3

AB = 2X + 2

Calculate X.

The area of the rectangle is equal to the length multiplied by the width.

Let's present the known data:

$24=3\times(2x+2)$

$24=6x+6$

We'll move 6 to the left side and maintain the appropriate sign:

$24-6=6x$

$18=6x$

We'll divide both sides by 6:

$x=3$

3

The area of the rectangle below is equal to 30.

AC = 3

AB = 2X

Calculate X.

The area of the rectangle is equal to its length multiplied by its width.

We begin by inserting the given data into this formula:

$30=3\times2x$

$30=6x$

Lastly we divide both sides by 6:

$x=5$

5

The area of the rectangle below is equal to 48.

AC = 4

AB = 2X

Calculate X.

The area of the rectangle is equal to the length multiplied by the width.

Let's begin by presenting the known data:

$48=4\times2x$

$48=8x$

Lastly let's divide both sides by 8:

$x=6$

6

The area of a rectangle is equal to 72.

AC = 2X

AB = 4X

Calculate X.

The area of the rectangle is equal to the length multiplied by the width.

Let's set up the known information:

$72=2x\times4x$

$72=8x^2$

Let's divide both sides by 8:

$9=x^2$

Let's take the square root:

$x=3$

3

The width of a rectangle is equal to$x$ cm and its length is equal to$\frac{x}{2}$ cm.

$x=4$

What is the area of the rectangle?

The area of a rectangle equals length times width

Let's put the data into the formula:

$S=x\times\frac{x}{2}=\frac{x^2}{2}$

Since we are given that x equals 4, let's substitute it into the formula accordingly:

$S=\frac{4^2}{2}=\frac{16}{2}=8$

8

The area of the rectangle below is equal to 72.

AC = X

AB = 2X

Calculate X.

The area of the rectangle is equal to the length multiplied by the width.

Let's set up the known data:

$72=x\times2x$

$72=2x^2$

Let's divide both sides by 2:

$36=x^2$

Let's take the square root:

$x=6$

6

The width of a rectangle is equal to $x^2$cm and its length is $x$cm.

$x=9$

Calculate the area of the rectangle.

The area of a rectangle is equal to length multiplied by width

Let's input the known data into the formula:

$S=x\times x^2$

Since we are given that x equals 9, let's substitute it into the formula:

$S=9\times9^2=9\times81=729$

729

The the area of the rectangle DBFH is 20 cm².

Work out the volume of the cuboid ABCDEFGH.

We know the area of DBHF and also the length of HF

We will substitute into the formula in order to find BF, let's call the side BF as X:

$4\times x=20$

We'll divide both sides by 4:

$x=5$

Therefore, BF equals 5

Now we can calculate the volume of the box:

$8\times4\times5=32\times5=160$

$160$ cm³

Rectangle ABCD has an area of 12 cm².

Calculate the volume of the cuboid ABCDEFGH.

Based on the given data, we can argue that:

$BD=HF=2$

We know the area of ABCD and also the length of DB

We'll substitute in the formula to find CD, let's call the side CD as X:

$2\times x=12$

We'll divide both sides by 2:

$x=6$

Therefore, CD equals 6

Now we can calculate the volume of the box:

$6\times2\times3=12\times3=36$

$36$

The width of a rectangle is equal to
$8$ cm and its length is $x$ cm.

The area of the rectangle is $32$ cm².

Calculate $x$.

The area of the rectangle equals length times width

Let's input the known data into the formula:

$32=8x$

Let's divide both sides by 8:

$x=4$

4

Given the rectangle ABCD

Given BC=X and the side AB is 4 timis greater than the side BC

The area of the rectangle is 64 cm².

Calculate the size of the side BC

The area of the rectangle equals:

$S=AB\times BC$

$64=AB\times X$

Since it is given that side AB is 4 times larger than side BC

We can state that:

$AB=4BC=4X$

Now let's substitute this information into the formula for calculating the area:

$64=4x\times x$

$64=4x^2$

Let's divide both sides by 4:

$16=x^2$

We'll take the square root and get:

$4=x$

In other words, BC equals 4

4

The width of a rectangle is equal to$x$ cm and its length is $x-4$ cm.

Calculate the area of the rectangle.

The area of the rectangle is equal to the length times the width:

$S=x\times(x-4)$

$S=x^2-4x$

$X^2-4X$$$

The width of a rectangle is equal to$2x$ cm and its length is $2x-8$ cm.

Calculate the area of the rectangle.

The area of a rectangle is equal to length multiplied by width

Let's input the known data into the formula:

$S=2x\times(2x-8)$

$S=2x\times2x-2x\times8$

$S=4x^2-16x$

$4X^2-16X$

The area of the rectangle below is equal to 22x.

Calculate x.

The area of the rectangle is equal to the length multiplied by the width.

Let's list the known data:

$22x=\frac{1}{2}x\times(x+8)$

$22x=\frac{1}{2}x^2+\frac{1}{2}x8$

$22x=\frac{1}{2}x^2+4x$

$0=\frac{1}{2}x^2+4x-22x$

$0=\frac{1}{2}x^2-18x$

$0=\frac{1}{2}x(x-36)$

For the equation to be equal, x needs to be equal to 36

$x=36$

The area of the square whose side length is 4 cm is
equal to the area of the rectangle whose length of one of its sides is 1 cm.

What is the perimeter of the rectangle?

After squaring all sides, we can calculate the area as follows:

$4^2=16$

Since we are given that the area of the square equals the area of the rectangle , we will write an equation with an unknown since we are only given one side length of the parallelogram:

$16=1\times x$

$x=16$

In other words, we now know that the length and width of the rectangle are 16 and 1, and we can calculate the perimeter of the rectangle as follows:

$1+16+1+16=32+2=34$

34

Given the rectangle ABCD

Given BC=X and the side AB is larger by 4 cm than the side BC.

The area of the triangle ABC is 8X cm².

What is the area of the rectangle?

Let's calculate the area of triangle ABC:

$8x=\frac{(x+4)x}{2}$

Multiply by 2:

$16x=(x+4)x$

Divide by x:

$16=x+4$

Let's move 4 to the left side and change the sign accordingly:

$16-4=x$

$12=x$

Now let's calculate the area of the rectangle, multiply the length and width where BC equals 12 and AB equals 16:

$16\times12=192$

192