The base of an isosceles triangle is 24 cm and its area is 60 cm2. Find its perimeter.

Mathematics

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The base of an isosceles triangle = 24 cm

Area of the triangle = 60 cm².

Let the height of the triangle be a.

Area of triangle = $\dfrac{1}{2}$ x base x height

⇒ 60 = $\dfrac{1}{2}$ x 24 x a

⇒ 60 = 12 x a

⇒ a = $\dfrac{60}{12}$

⇒ a = 5

Since, the triangle is isosceles, the height divides the base into two equal halves. Then applying Pythagoras theorem,

Hypotenuse² = Base² + Height²

= $\Big(\dfrac{24}{2}\Big)^2$ + 5²

= 12² + 5²

= 144 + 25

= 169

⇒ Other side = $\sqrt{169}$

= 13

Perimeter of triangle = sum of all sides

= 24 + 13 + 13

= 50 cm

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