Square of sum: Using quadrilaterals

Question 1

Given the rectangle ABCD

AB=X

The ratio between AB and BC is $\sqrt{\frac{x}{2}}$

We mark the length of the diagonal A the rectangle in m

Check the correct argument:

Question 2

Given the trapezoid where the height is equal to the sum of the two bases.

It is known that the difference between the large base and the small base is 5

We will mark the small base with X

Express the area of the trapezoid using X

Question 3

Given two squares, one side of the squares is larger by 2 than the other. The area of the large square is larger than the perimeter of the small square by 20

Find the length of the small square

Question 4

Given a rectangle whose side is greater by 6 than the other side. We mark the area of the rectangle with S

What is the correct argument?

Question 5

Given a square of side length X

We will mark the area of the square by S and the perimeter of the square by P

Check the correct statement

Examples with solutions for Square of sum: Using quadrilaterals

Exercise #1

Given the rectangle ABCD

AB=X

The ratio between AB and BC is $\sqrt{\frac{x}{2}}$

We mark the length of the diagonal A the rectangle in m

Check the correct argument:

Video Solution

Step-by-Step Solution

Given that:

$\frac{AB}{BC}=\sqrt{\frac{x}{2}}$

Given that AB equals X

We will substitute accordingly in the formula:

$\frac{x}{BC}=\frac{\sqrt{x}}{\sqrt{2}}$

$x\sqrt{2}=BC\sqrt{x}$

$\frac{x\sqrt{2}}{\sqrt{x}}=BC$

$\frac{\sqrt{x}\times\sqrt{x}\times\sqrt{2}}{\sqrt{x}}=BC$

$\sqrt{x}\times\sqrt{2}=BC$

Now let's focus on triangle ABC and use the Pythagorean theorem:

$AB^2+BC^2=AC^2$

Let's substitute the known values:

$x^2+(\sqrt{x}\times\sqrt{2})^2=m^2$

$x^2+x\times2=m^2$

We'll add 1 to both sides:

$x^2+2x+1=m^2+1$

$(x+1)^2=m^2+1$

Answer

$m^2+1=(x+1)^2$

Exercise #2

Given the trapezoid where the height is equal to the sum of the two bases.

It is known that the difference between the large base and the small base is 5

We will mark the small base with X

Express the area of the trapezoid using X

Video Solution

Answer

$\frac{1}{2}\lbrack4x^2+20x+25\rbrack$

Exercise #3

Given two squares, one side of the squares is larger by 2 than the other. The area of the large square is larger than the perimeter of the small square by 20

Find the length of the small square

Video Solution

Answer

Exercise #4

Given a rectangle whose side is greater by 6 than the other side. We mark the area of the rectangle with S

What is the correct argument?

Video Solution

Answer

9+S equal to the smaller side plus 3 squared (the two squared).

Exercise #5

Given a square of side length X

We will mark the area of the square by S and the perimeter of the square by P

Check the correct statement

Video Solution

Answer

$P+S+4=(x+2)^2$

Question 1

Shown below is the rectangle ABCD.

AB = y

AD = x

Express the square of the sum of the sides of the rectangle using the area of the triangle DEC.

Exercise #6

Shown below is the rectangle ABCD.

AB = y

AD = x

Express the square of the sum of the sides of the rectangle using the area of the triangle DEC.

Video Solution

Answer

$(x+y)^2=4s\lbrack\frac{s}{y^2}+\frac{s}{x^2}+1\rbrack$