Isosceles triangle with perimeter 32 cm and equal sides 5/6 of base:\nFind the area (in cm²).

Difficulty: Medium

39
48
57
64
None of these

Correct Answer: 48

Explanation:

Introduction / Context:
Use the perimeter condition to find the base and equal sides, then compute height via Pythagoras and the area.

Given Data / Assumptions:

Perimeter = 32 cm.
Let base = b; each equal side = (5/6)b.

Concept / Approach:
Perimeter: b + 2*(5b/6) = 32 ⇒ solve b. Height comes from splitting the base and using right triangles.

Step-by-Step Solution:

1) b + (10b/6) = 32 ⇒ (16b/6) = 32 ⇒ b = 12 cm.2) Equal side = (5/6)*12 = 10 cm.3) Height h = √(10^2 − (12/2)^2) = √(100 − 36) = 8 cm.4) Area = (1/2)*b*h = 0.5*12*8 = 48 cm².

Verification / Alternative check:
Perimeter check: 12 + 10 + 10 = 32.

Why Other Options Are Wrong:
39, 57, 64 arise from computation errors in b or h.

Common Pitfalls:
Not halving the base when using Pythagoras for an isosceles triangle.

Isosceles triangle with perimeter 32 cm and equal sides 5/6 of base:\nFind the area (in cm²).

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