Question

Consider the following two statements

Statement-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 $=\sqrt{\left.s(s-a\right)(s-b)(s-c)}$

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 statements 1 and 2 are false.

Answer 1

The correct option is A

Statement 1 is true and Statement 2 is false

Explanation for correct option:

A:

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

In a right angled triangle two sides containing right angle means perpendicular and the base.
Area of the triangle $=\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times \text{base}\times \text{perpendicular}$
$=\frac{\text{Product of the two sides containing right angle}}{2}$

Hence the statement 1 is true.

Step 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 $=\sqrt{\left.s(s-a\right)(s-b)(s-c)}$

Step 2: Heron's formula:

As we know,

We can determine the area of triangle by using Heron's formula:

As per Heron's formula:

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

Where, $s=\frac{a+b+c}{2}$, and $a,b,c$ are sides of triangle.

In Heron's formula ' $s$ ' means the half of the perimeter not only 'perimeter'.

So, statement 2 is false.

Hence option A is correct.