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

Answer:

The area of square 2 is 130 units square

Step-by-step 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