Question:
Euclid has a triangle with longest side 20, another side 10, and area 80. What is the exact length of the third side?
Euclid has a triangle with longest side 20, another side 10, and area 80. What is the exact length of the third side?
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Heron’s formula works for all triangles when given two sides and area.
Updated On: Aug 4, 2025
- $\sqrt{260}$
- $\sqrt{250}$
- $\sqrt{240}$
- $\sqrt{270}$
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The Correct Option is D
Solution and Explanation
Let third side = $x$. By Heron’s formula: $s = \frac{20+10+x}{2}$, area $=80=\sqrt{s(s-20)(s-10)(s-x)}$. Square both sides and solve: $6400 = s(s-20)(s-10)(s-x)$. Substituting and solving yields $x=\sqrt{270}$.
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