Question

The areas of the squares formed by the side lengths of the triangles are given for each triangle below. Which triangles are right triangles? Check all that apply. (Figures are not drawn to scale.)

Answer 1

B and D are your answers

Answer 2

Option B.

`9 +16 = 25`

Option D

`64 +225 = 289`

Explanation:

According to the Pythagorean theorem, for any rectangular triangle:

The sum of the square of its opposite side plus the square of its adjacent side is equal to the square of its hypotenuse.

All the rectangles shown in the figures are square, therefore, the area of these is equal to the square of one of its sides.

Therefore, to find out which of the triangles is a right triangle, add the square of its opposite side plus the square of its adjacent side and verify that it is equal to the hypotenuse squared.

Option A.

`6 + 8 = 18`

Equality is not satisfied.

Option B.

`9 +16 = 25` -------- Equality is satisfied t, it is a straight triangle.

Option C

`24 +7 = 25`

Equality is not satisfied.

Option D

`64 +225 = 289` ------- Equality is satisfied, it is a straight triangle.

Option E

`10 +24 = 26`

Equality is not satisfied..