Question

Each equal side of an isosceles triangle is 3cm less than the unequal side. The height of the perpendicular from the vertex to the unequal side is 3cm less than the equal side. If the area of the isosceles triangle is 108cm², find the perimeter of the triangle.

Answer 1

Let the unequal side of the Isosceles triangle = x
Then the equal side of the Isosceles triangle = x - 3
And the perpendicular to the unequal side from the opposite vertex = x - 6

We know that, Area of a Triangle

= `(1)/(2)"b.h"  "i.e"(1)/(2)("Base" xx "Height")`

∴ Area of the Isosceles Triangle

= `(1)/(2) xx(x - 6)`
= 108
⇒ x² - 6x = 216
⇒ x² - 6x - 216 = 0
⇒ x² - 6x + 9 - 9 - 216 = 0
⇒ (x - 3)² = 225
⇒ x - 3 = 15
⇒ x = 18
⇒ x - 3 = 15
⇒ Perimeter
= 18 + 15 + 15
= 48cm.