The perimeter of an isosceles triangle is 64 cm. The ratio of the equal side to its base is 5 : 6. Find the area of the triangle.
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Step by Step Explanation:
- Let's assume, the lengths of the base and the equal sides of the isosceles triangle are b cm and x cm respectively.
Following figure shows the isosceles triangle ABC,
The ratio of the equal side to its base is 5 : 6.
By cross multiplying, we get:
b = ------(1)
- According to the question, the perimeter of the isosceles triangle ABC = 64 cm
Therefore, x + x + b = 64
⇒ 2x + = 64 [From equation (1), b = ]
⇒ = 64
⇒ 10x + 6x = 320
⇒ 16x = 320
⇒ x = 20 cm
- Putting the value of x in equation (1), we get:
b = = 24 cm
- The area of the isosceles triangle ABC can be calculated using Heron's formula, since all sides of the triangle are known.
S = = 32 cm
The area of the isosceles triangle ABC = √S(S - AB)(S - BC)(S - CA)
= √32(32 - 24)(32 - 20)(32 - 20)
= 192 cm2
- Thus, the area of the triangle is 192 cm2.