Question

The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle. 12 yd, 14 yd, 16 yd 15 km, 20 km, 25 km 45 mm, 60 mm, 75 mm

Answer 1

Given

sides of a triangles

Find

Determine whether each triangle is a right triangle.

Explanation

use the pythagoras theorem for right triangles.

According to the pythagoras theorem , the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs of the triangle.

a) 12 yd, 14 yd, 16 yd

so ,

$\begin{gathered} 16^2=12^2+14^2 \\ 256=144+196 \\ 256\ne340 \end{gathered}$

hence it is not right triangle.

b) 15 km, 20 km, 25 km

$\begin{gathered} 25^2=20^2+15^2 \\ 625=400+225 \\ 625=625 \end{gathered}$

hence it is a right triangle.

c) 45 mm, 60 mm, 75 mm

$\begin{gathered} 75^2=45^2+60^2 \\ 5625=2025+3600 \\ 5625=5625 \end{gathered}$

hence it is a right triangle.

Final Answer

Hence ,

a) it is not right triangle

b) it is a right triangle

c) it is a right triangle