Question

The perimeter of an isosceles triangle is 32 cm. The base is 2 cm more than each of the equal sides. Find the area of the triangle.

Answer 1

Given:

• Perimeter of isosceles triangle = 32 cm
• Base = 2 cm more than each of the equal sides

Step 1: Let each equal side be x cm.

Then the base = x + 2 cm.

Step 2: Write the perimeter equation:

2x + (x + 2) = 32

3x + 2 = 32 

3x = 30 

x = 10 cm 

So, the equal sides are 10 cm each and the base is 10 + 2 = 12 cm.

Step 3: Find the height of the triangle.

Drop a perpendicular from the apex opposite the base to the base, dividing the base into two equal parts of 6 cm each.

Using the Pythagorean theorem in one of the right triangles formed:

Height² + 6² = 10²

Height² + 36 = 100

Height² = 64

Height = 8 cm

Step 4: Find the area of the triangle:

A = `1/2` × base × height

= `1/2 xx 12 xx 8`

= 48 cm²

The area of the triangle is 48 cm².