Question

Assertion : Area of a triangle $=\sqrt{\left.s(s-a\right)(s-b)(s-c)}$ where $a,bandc$ are the sides of the triangle and $s=\frac{a+b+c}{2}$

Reason: Area of a triangle $=\frac{1}{2}\times base\times height$.

Which of the following is correct?

• A. A is true and $R$ is false
• B. $\mathrm{A}$ is false and $R$ is true.
• C. Both $\mathrm{A}$ and $\mathrm{R}$ are true and $\mathrm{R}$ is the correct explanation of $A$.
• D. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$

Answer 1

The correct option is D

Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$

Explanation for correct option:

D:

Step1: Assertion : Area of a triangle $=\sqrt{\left.s(s-a\right)(s-b)(s-c)}$ where $a,bandc$ are the sides of the triangle and $s=\frac{a+b+c}{2}$

If a side of a triangle is $a,b$and $c$.

By heron's formula,

$s=\frac{a+b+c}{2}$

Area of a triangle is ,

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

Hence, Assertion is true.

Step 2: Reason: Area of a triangle $=\frac{1}{2}\times base\times height$.

the total region that is enclosed by the three sides of any particular triangle.

Basically, it is equal to half of the base times height.

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

Hence, Reason is true.

Both Assertion and Reason statements are true but they are two different ways of calculating the area of triangle.

Hence option d is correct.