Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

Two equal sides of an isosceles triangle are $13 cm$ each and its perimeter is $36 cm$ . Find the area of the triangle.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

20 cm 2

30 cm 2

40 cm 2

60 cm 2

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The given sides of the isosceles triangle are:
a = 13cm, b = 13cm and let, c = x cm.
Also, the perimeter of the triangle = 36 cm

\Rightarrow a + b + c = 36

\Rightarrow 13 + 13 + x = 36

\Rightarrow 26 + x = 36

\Rightarrow x = 36 - 26

\Rightarrow x = 10 cm

∴ The sides are a = 13 cm, b = 13 cm c = 10 cm .

Now, semi-perimeter, s =

\frac{a + b + c}{2} = \frac{13 + 13 + 10}{2} = \frac{36}{2} = 18 cm

.
By Heron’s Formula, Area of triangle =

S (s − a) (s − b) (s − c)

⇒ 18 (18 − 13) (18 − 13) (18 − 10) ⇒ 18 (5) (5) (8) ⇒ 3600 ⇒ (60) 2 ⇒ 60 c m 2

So, the required area of the triangle is

60 c m 2

.
Hence, the correct option is 4.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE