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# Area of an isosceles triangle is 48 cm². If the altitude corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.

**Solution:**

Given, the area of an __isosceles triangle__ is 48 cm².

The altitude corresponding to the base of the triangle is 8 cm.

We have to find the __perimeter of the triangle__.

Consider an isosceles triangle ABC,

Here, AB = AC

__Area of triangle__ = 1/2 × base × height

Area of ∆ABC = 1/2 × BC × AD

48 = 1/2 × BC × 8

48 = 4BC

BC = 48/4

BC = 12 cm

AD is the __perpendicular bisector__ of BC

So, BD = CD = 12/2 = 6 cm

Considering right angled triangle ADB,

By using __Pythagoras theorem__,

AB² = AD² + BD²

AB² = (8)² + (6)²

AB² = 64 + 36

AB² = 100

Taking square root,

AB = 10 cm

Perimeter of triangle ABC = AB + BC + AC

= 10 + 12 + 10

= 20 + 12

= 32 cm

Therefore, the perimeter of triangle is 32 cm

**✦ Try This: **Area of an isosceles triangle is 88 cm². If the altitude corresponding to the base of the triangle is 16 cm, find the perimeter of the triangle.

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 11

**NCERT Exemplar Class 7 Maths Chapter 9 Problem 88**

## Area of an isosceles triangle is 48 cm². If the altitude corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.

**Summary:**

Area of an isosceles triangle is 48 cm². If the altitude corresponding to the base of the triangle is 8 cm, the perimeter of the triangle is 32 cm

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