Just a simple problem of triangle

Geometry Level pending

What is the area of a triangle, whose side lengths are 7, 9, and 14? Round your answer to the nearest integer.


The answer is 27.

Shintaro Inaba by Shintaro Inaba , 17, Japan

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1 solution

Chew-Seong Cheong
Jan 11, 2020

By Heron's formula , the area of the triangle is:

A = s ( s − a ) ( s − b ) ( s − c ) where a = 7 , b = 9 , c = 14 = 15 ( 8 ) ( 6 ) ( 1 ) and s = a + b + c 2 = 15 = 720 ≈ 27 \begin{aligned} A & = \sqrt{s(s-a)(s-b)(s-c)} & \small \blue{\text{where }a = 7, b=9, c= 14} \\ & = \sqrt{15(8)(6)(1)} & \small \blue{\text{and }s = \frac {a+b+c}2 = 15} \\ & = \sqrt{720} \approx \boxed{27} \end{aligned}

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