Question

decide if each of the triangles is a right triangle. the figures are not drawn to scale.
triangle i (sides 15, 30, 39)
triangle ii (sides 20, 48, 52)
which triangles are right triangles?
a. triangle i only
b. triangle i and triangle ii
c. triangle ii only
d. neither triangle i nor triangle ii

Explanation:

Step1: Test Triangle I via Pythagoras

Check if $30^2 + 15^2 = 39^2$

$$\begin{align*} 30^2 + 15^2 &= 900 + 225 = 1125\\ 39^2 &= 1521 \end{align*}$$

$1125
eq 1521$, so not right.

Step2: Test Triangle II via Pythagoras

Check if $48^2 + 20^2 = 52^2$

$$\begin{align*} 48^2 + 20^2 &= 2304 + 400 = 2704\\ 52^2 &= 2704 \end{align*}$$

$2704 = 2704$, so it is right.

Answer:

C. Triangle II only