the ratio of the equal sides to the base of an iscosceles triangle is 3:1.if the perimeter of the triangle is 28cm.then find its area
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Step-by-step explanation:
The perimeter of an isosceles △=32cm .
Given that the ratio of the equal side to its base is 3:2.
So the ratio of all three sides of the isosceles △=3:3:2
Sum of the ratios = 3+3+2=8
Length of equal side =
8
3
×32=3×4=12
Length of the base =
8
2
×32=2×4=8
According to Heron's formula, Area of an isosceles △ with equal sides a & base b
=
4
1
×b×
(4a
2
−b
2
)
∴ Area of the given isosceles triangle, where a=12 & b=8
=
4
1
×8×
(4×12
2
)−8
2
=2×
(4×144)−64
= 2×
576−64
= 2×
512
=2×
2×16×16
=2×16×
2
= 32
2
∴m=2
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