Question

Consider the following two statements

Statement-1: If $s=\frac{a+b+c}{2}$, where $a,b,c$ are the sides of a triangle then the area of the triangle is $=\sqrt{(s-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})}$

Statement-2: We can calculate the area of a quadrilateral if its four sides and one diagonal is given.

Which of the following is correct?

• 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 B

Statement 1 is false and Statement 2 is true.

Explanation for correct option:

B:

Step 1: Statement-1: If $s=\frac{a+b+c}{2}$, where $a,b,c$ are the sides of a triangle then the area of the triangle is $=\sqrt{(s-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})}$

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.

Therefore statement-1 is false.

Step 2: Statement-2: We can calculate the area of a quadrilateral if its four sides and one diagonal is given.

As we know,

Area of quadrilateral $=\frac{1}{2}\times diagonallength\times sumofthelengthoftheperpendicularsdrawnfromtheremainingtwovertices.$

Thus statement 2 is correct.

Hence option B is correct.