Question

Adam needs to build a shed and he can only use triangular frames that form a right

triangle for the corner walls. Which of the following dimensions for a triangular
frame should Adam use?
A 50 in., 110 in., 130 in.
B 25 in., 60 in., 65 in.
C 40 in., 44 in., 58 in.
D 130 in., 50 in, 60 in.

Answer 1

Option B: 25 inches, 60 inches and 65 inches is the correct answer.

Explanation:

We will use Pythagorean theorem to find out the dimensions that Adam should use.

A. 50 in, 110 in and 130 in

Using Pythagorean theorem;

`a^2+b^2=c^2 \\(50)^2 + (110)^2 = (130)^2\\2500 + 12100 = 16900\\14600\\eq 16900`

These dimensions will not form a right triangle.

B. 25 in, 60 in, and 65 in

`(25)^2 + (60)^2=(65)^2\\625+3600= 4225\\4225=4225`

These dimensions of the frame will form a right triangle.

C. 40 in., 44 in., 58 in.

`(40)^2+(44)^2=(58)^2\\1600+1936=3364\\3536\\eq 3364`

These dimensions will not form a right angled triangle.

D. 130 in., 50 in, 60 in

The larger dimension represents the hypotenuse in right angled triangle.

`(50)^2+(60)^2=(130)^2\\2500+3600=16900\\6100\\eq 16900`

These dimensions will not form a right angled triangle.

Hence,

Option B: 25 inches, 60 inches and 65 inches is the correct answer.