The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
Solution:
Given, the perimeter of an isosceles triangle is 32 cm
The ratio of the equal side to its base is 3 : 2
We have to find the area of the triangle
We know that an isosceles triangle has two equal sides.
Le the sides be AB = BC = 3x and AC = 2x
Perimeter = equal side + equal side + base
32 = 3x + 3x + 2x
32 = 8x
x = 32/8
x = 4 cm
So, AB = BC = 3(4) = 12 cm
AC = 2(4) = 8 cm
Area of isosceles triangle = a/4 √4b² - a²
Where, a = base
b = equal side
Here, a = 8 cm and b = 12 cm
Area = 8/4 √4(12)²-(8)²
= 2√4(144) - 64
= 2√576 - 64
= 2√512
= 2√64 × 8
= 2 × 8(√8)
= 16(2√2)
= 32√2 cm²
Therefore, the area of isosceles triangle is 32√2 cm²
✦ Try This: The perimeter of an isosceles triangle is 56 cm. The ratio of the equal side to its base is 2 : 5. Find the area of the triangle.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12
NCERT Exemplar Class 9 Maths Exercise 12.3 Problem 4
The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
Summary:
The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. The area of the triangle is 32√2 cm²
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