Question

The sides of a triangle are in the proportion of 2 : 3 : 5 and its perimeter is 200 cm. The area of this triangle is __________ cm^2.

(a) 375 \(\sqrt{23}\)

(b) 375 \(\sqrt{21}\)

(c) 345 \(\sqrt{23}\)

(d) 345 \(\sqrt{21}\)

This question was posed to me in an online interview.

Asked question is from Heron’s Formula & Area of a Triangle by Heron’s Formula topic in section Heron’s Formula of Mathematics – Class 9

Answer 1

Correct choice is (a) 375 \(\sqrt{23}\)

Explanation: Let the side of a triangles be a = 2x, b = 3x and c = 5x.

Perimeter of the triangle is 200 cm.

Therefore a + b + c = 2x + 3x + 5x = 200

10x = 200

Hence, x = 20

a = 2x = 2(20) = 40 cm

b = 3x = 3(30) = 90 cm

c = 5x = 5(20) = 100 cm

Now, s = \(\frac{a+b+c}{2}=\frac{40+90+100}{2} = \frac{230}{2}\) = 115

According to heron’s formula, area of the triangle = \(\sqrt{s*(s-a)*(s-b)*(s-c)}\)

= \(\sqrt{115*(115-40)*(115-90)*(115-100)}\)

= \(\sqrt{115*75*25*15}\)

= \(375 \sqrt{23}\)