Question

A triangle PQR is constructed with PQ = 10 cm, PR = 8 cm and $\angle P={90}^{\circ }$. Identify the correct classification of $\Delta$ PQR.

• A. Based on sides - Scalene ; Based on angle - Right angled
• B. Based on sides - Isosceles; Based on angle - Acute angled
• C. Based on sides - Scalene ; Based on angle - Acute angled
• D. Based on sides - Isosceles ; Based on angle - Right angled

Answer 1

The correct option is A Based on sides - Scalene ; Based on angle - Right angled

From the given measurements, the triangle is a right-angled triangle.

The third side can be calculated by using Pythagoras property.
$\Rightarrow P{Q}^2=P{R}^2+Q{R}^2$
$\Rightarrow {10}^2=8^2+Q{R}^2$
$\Rightarrow Q{R}^2={10}^2-8^2$
$\Rightarrow Q{R}^2=100-64$
$\Rightarrow Q{R}^2=36=6^2$
$\Rightarrow QR=6cm$

Hence, from the measurements of the other two sides, the length of the third side is 6 cm. Therefore. the triangle is a scalene right angled triangle.