Area of a Rectangle: Worded problems

What is the length of the second side in a rectangle, given that the sum of the 2 opposite sides is 14 cm and the area of the rectangle is 21 cm²?

If we are given that two opposite sides of the rectangle sum to 14

and in a rectangle, each pair of opposite sides are equal to each other, we will calculate the size of each one as follows:

$14:2=7$

We will call the other two opposite sides y and find the unknown as follows:

$7\times y=21$

We will divide both sides by 7 and get:

$y=3$

3

The area of a rectangle is 256 cm².

One side is 4 times longer than the other.

What are the dimensions of the rectangle?

To find the area of the rectangle, we multiply the length by the width.

According to the data in the statement, one side will be equal to X and the other side will be equal to 4X

Now we replace the existing data:

$S=x\times4x$

$256=4x^2$

We divide the two sections by 4:

$64=x^2$

We extract the square root:

$x=\sqrt{64}=8$

If we said that one side is equal to x and the other side is equal to 4x and we know that x=8

From here we can conclude that the sides of the rectangle are equal:

$8,8\times4=8,32$

8 x 32

Joseph is building a pool.

He buys tiles with sides measuring 10 cm by 5 cm.

The size of Joseph's pool is 850 cm².

How many tiles does Joseph need?

First, let's calculate the area of the tile by multiplying length and width:

$10\times5=50$

Now let's calculate how many tiles fit in the given pool area - 850 cm²:

$850:50=17$

Therefore, Yossi needs 17 tiles

$17$

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

The length of the side of a square is X cm

(x>3)

Extend one side by 3 cm and shorten an adjacent side by 3 cm to obtain a rectangle.

Express the area of the rectangle using x.

$x^2-9\left(\operatorname{cm}²\right)$

The length of the side of the square $x+1$ cm

(x>3)

We extend one side by 1 cm and shorten an adjacent side by 1 cm, and we obtain a rectangle.

What is the area of the rectangle?

$x^2+2x$

The length of the square is equal to $x$ cm

(x>1) We extend one side by 3 cm and shorten an adjacent side by 1 cm and we obtain a rectangle,

What is the length of the side of the given square if it is known that the two areas are equal?

$x=\frac{3}{2}cm$

The side length of a square is X cm

(x>3)

We extend one side by 3 cm and shorten an adjacent side by 3 cm, and we get a rectangle.

Which shape has a larger area?

The square

Gerard plans to paint a fence 7X meters high and 30X+4 meters long.

Gerardo paints at a rate of 7 m² per half an hour.

Choose the expression that represents the time it takes for Gerardo to paint one side of the fence.

$15x^2+2x$ hours