Question

Consider the following two statements

Statements - 1: The area of a right angled triangle
$=\frac{\text{Product of the two sides containing right angle}}{2}$

Statement - 2: If the perimeter of a triangle is s and the sides of the triangle are a, b and c respectively then the area of the triangle
$=\sqrt{s(s-a)(s-b)(s-c)}$

Which of the following is true?

• A. Statement 1 is true and Statement 2 is false.
• B. Statement 1 is false and Statement 2 is true.
• C. Both the statements 1 and 2 are true.
• D. Both the ststements 1 and 2 are false.

Answer 1

The correct option is A

Statement 1 is true and Statement 2 is false.

In a right-angled triangle, two sides containing right angle is the perpendicular and the base.

Area of the triangle = $\frac{1}{2}$ $\times$ base $\times$ height

= $\frac{1}{2}$ $\times$ base $\times$ perpendicular

= $\frac{\text{Product of the two sides containing right angle}}{2}$

$\therefore$ Statement 1 is true.

In Heron’s formula ‘s’ stands for semiperimeter.

Hence, Statement 2 is false.