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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