Question

What is the area of the triangle having sides equal to 10 cm, 16 cm and 24 cm?

(a) \(25\sqrt{15} cm^2\)

(b) \(35\sqrt{17} cm^2\)

(c) \(15\sqrt{13} cm^2\)

(d) \(15\sqrt{15} cm^2\)

I got this question in an international level competition.

Enquiry is from Heron’s Formula & Area of a Triangle by Heron’s Formula topic in portion Heron’s Formula of Mathematics – Class 9

Answer 1

The correct option is (d) \(15\sqrt{15} cm^2\)

Easy explanation: a = 10, b = 16 and c = 24

s = \(\frac{a+b+c}{2}=\frac{10+16+24}{2} = \frac{50}{2}\) = 25

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

= \(\sqrt{25*(25-10)*(25-16)*(25-24)}\)

= \(\sqrt{25*15*9*1}\)

= \(15\sqrt{15} cm^2\)