Question

If the area of square 1 is 250 units squared, and the area of square 3 is 120 units squared, what is the area if square 2? Explain your reasoning.

Answer 1

The area of square 2 is 130 units square

Explanation:

see the attached figure to better understand the problem

we know that

The area of a square is

`A=b^(2)`

where

b is the length side of the square

Let

b1 ----> the length side of square 1

b2 ----> the length side of square 2

b3 ----> the length side of square 3

Applying the Pythagoras Theorem

`b1^(2)=b2^(2)+b3^(2)` -----> equation A

we have

`A1=250\ units^2`

`A3=120\ units^2`

Remember that

`A=b^(2)`

so

`A1=b1^2=250\ units^2`

`A3=b3^2=120\ units^2`

substitute in the equation A and solve for b2^2

`250=b2^(2)+120`

`b2^(2)=250-120`

`b2^(2)=130`

`A2=b2^(2)`

therefore

The area of square 2 is 130 units square