Question

The perimeter of an isosceles triangle is 42 cm and its base is (3/2) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

Answer 1

We are given that and its base is (3/2) times each of the equal sides. We are asked to find out the length of each side, area of the triangle and height of the triangle. In this case ‘height’ is the perpendicular distance drawn on the base from the apposite vertex.

In the following triangle ΔABC

BC = a, AC = b, AB = c and AB = AC

Let the length of each of the equal sides be x and a, b and c are the side of the triangle. So,

Since .This implies that,

Therefore all the sides of the triangle are:

All the sides of the triangle are 18 cm, 12 cm, and 12 cm.

Whenever we are given the measurement of all sides of a triangle, we basically look for Heron’s formula to find out the area of the triangle.

If we denote area of the triangle by Area, then the area of a triangle having sides a, b, c and s as semi-perimeter is given by;

Where,

To calculate area of the triangle we need to find s:

The area of the triangle is:

Now we will find out the height, say H. See the figure, in which AD = H

So,