Question

An isosceles triangle has perimeter 36 cm. If each of the equal sides is 10 cm, then the area of the triangle is _____${\text{cm}}^2$

• A. 48
• B. 38
• C. 44
• D. 45

Answer 1

The correct option is A

48

Let the length of the unequal side be $x$ cm.

Then

$10+10+x=36$

$x=36-20=16$

We know the altitude bisects the base in an isosceles $△$

$\therefore$ height $AD\left(h\right)=6cm$ $(6,8,10\text{- Pythagorean Triplet})$

Area of $△=\frac{1}{2}\times \text{base}\times \text{height}=\frac{1}{2}\times 16\times 6$

$=48c{m}^2$