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
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
⇒s−a=75 cm−25 cm=50 cm
⇒s−b=75 cm−60 cm=15 cm
⇒s−c=75 cm−65 cm=10 cm
By Heron's formula,
Area of triangle, Δ=√s(s−a)(s−b)(s−c)
⇒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.