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

Answer:

Option B.

$9 +16 = 25$

Option D

$64 +225 = 289$

Step-by-step 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..

Answer 2

Answer:

Options B and D are the right angle triangles.

Step-by-step explanation:

We know as per Pythagoras theorem in a right angle triangle

Hypotenuse² = Base² + height²

So by this theorem we will check each option for the right angle triangles.

Option A.

6 + 8 = 14 ≠ 10

Therefore, option A is not a right angle triangle.

Option B.

9 + 16 = 25

So option B is a right angle triangle.

Option C.

7 + 24 = 31 ≠ 25

Option C. is not a right angle triangle.

Option D.

64 + 225 = 289

Option D is a right angle triangle.

Option E.

10 + 24 ≠ 26

Therefore, option E. is not a right angle triangle.

Options B, D are the right angle triangles.