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Question

The sides of a triangle are in the ratio 5:12:13 and its perimeter is 150 cm. The area of the triangle is

(a) 375 cm2

(b) 750 cm2

(c) 250 cm2

(d) 500 cm2

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Solution

Given:

The ratio of the sides of triangle =5:12:13

The sides of the triangle are 5x, 12x and 13x.

Perimeter of thr triangle =150 cm

5x,+12x+13x=150 cm

30x=150 cm

x=150 cm30

x=5 cm

Therefore, the sides are

a=5×5 cm=25 cm

b=12×5 cm=60 cm

c=13×5 cm=65 cm

Perimeter 2s=150 cm

s=150 cm2=75 cm

sa=75 cm25 cm=50 cm

sb=75 cm60 cm=15 cm

sc=75 cm65 cm=10 cm

By Heron's formula,

Area of triangle, Δ=s(sa)(sb)(sc)

Δ=(75 cm)×(50 cm)×(15 cm)×(10 cm)

Δ=75×50×15×10 cm2

Δ=25×3×25×2×5×3×5×2 cm2

Δ=25×5×3×2 cm2

Δ=750 cm2

Hence, Option B is correct.


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