Question

Please help me out here :’(

Answer 1

Explanation:

We are going to use the areas given to find the lengths of the sides of each of their respective squares. For the purple square, the area is 35 units squared. Because the formula for the area is A = s * s, then we can fill in the value for the area and solve for s, the side length, of the purple square.

`35=s^2` and

`s=√(35)`. That side length also serves as the height of the right triangle. Now on to the blue square on the bottom. It has an area of 50 units squared, so

`50=s^2` and

`s=√(50)`. We could feasibly simplify that, but it's not necessary, really. That side serves as the base of the right triangle. Now we can use Pythagorean's Theorem to find the length of the hypotenuse of the right triangle, which also serves as the side of the big blue square. We will call the side of the big blue square x.

`x^2=(√(35))^2+(√(50))^2` and

`x^2=35+50` and

`x^2=85` and

`x=√(85)`. That is the side length of the large blue square. The area for the square is s * s, and since we know the side length to be √85:

`A=(√(85))(√(85))` so

A = 85 units squared