Question

The areas of the squares adjacent to two sides of a right triangle are shown below.

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

Answer 1

85

Explanation:

We can use the Pythagorean theorem (a^2+b^2=c^2) to find the area of square adjacent to the third side.

Area of a square=side^2

So, we can substitute the areas of the squares that share side lengths with the triangle for a^2, b^2, and c^2 in the Pythagorean theorem.

For example, in the diagram above, the area of the square that shares a side with side length a is 35 square units. So, a^2=35.

Let's fill in the remaining values:

a^2 + b^2 = x^2

35+50-x^2
85=x^2
The area of the square adjacent to the third side of the triangle is 85 units^2.

Answer 2

`85\:\mathrm{units^2}`

Explanation:

All side lengths of a square are equal. The three squares create a right triangle, and the hypotenuse of this triangle represents the side length of the square.

All right triangles must follow the Pythagorean Theorem
`a^2+b^2=c^2` where
`c` is the hypotenuse of the triangle.

Therefore, let
`h` be the side length of this largest square. Since the area of a square with side length
`s` is given by
`s^2`,
`h^2` will represent the area of the square:

`√(35)^2+√(50)^2=h^2=\boxed{85\:\mathrm{units^2}}`