Question

What is the area of the square adjacent to the third side of the triangle?

If known could u answer the other as well ?

Answer 1

85 units^2 = Area of Blue Square

and

x = 5 units

Explanation:

To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.

Since we know the area of a square is the side length multiplied by itself (or the side length squared),
`√(35)` is the side length of the pink square and
`√(50)` is the side length of the green square.

That means a =
`√(35)` and b =
`√(50)` , so...

`(√(35) )^(2) + (√(50))^(2) = c^(2)`

35 + 50 = c^2

85 = c^2

`√(85) = c`

Now we need to square the square root of 85 to find the area of the blue square.

`(√(85))^(2) = Area of blue square`

85 units^2 = Area of Blue Square

To solve the other question we use the same formula again.

`x^2 + 12^2 = 13^2\\x^2 +144 = 169\\-144\\x^2 = 25\\x=√(25) \\x=5`

x = 5 units