Question

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

• A. 48
• B. 38
• C. 44
• D. 45

Answer 1

The correct option is A

48

Let $△$ABC be the isosceles triangle with AB = AC.
Construction: AD is the perpendicular drawn from vertex A to BC.
Let the length of the side BC be $x$ cm.

Given, perimeter of the triangle = 36
Perimeter = sum of all sides
= $10+10+x=36$
$\Rightarrow x=16cm$

We know that the altitude drawn from the common vertex of equal sides in an isosceles triangle, bisects the third side.
So, BD = $\frac{1}{2}$BC = 8 cm

Now, AB = 10 cm, BD = 8 cm
Therefore, AD(height) = 6 cm (Since ABD is a right triangle and 6, 8, 10 form a pythagorean triplet)

$\therefore$ height $\left(h\right)=6cm$

Area of triangle ABC
$=\frac{1}{2}\times base\times height=\frac{1}{2}\times 16\times 6$
$=48c{m}^2$