What About The Third Side?

Geometry Level 1

Which of the following triangles has the largest area?

An acute isosceles triangle with 2 side lengths 1,
A right isosceles triangle with 2 side lengths 1, or
An obtuse isosceles triangle with 2 side lengths 1.

The acute isosceles triangle The right isosceles triangle The obtuse isosceles triangle

1 solution

Rishabh Jain
Apr 1, 2016

Area of triangle with two sides $1$ and included angle $A$ is given by :

$\color{#D61F06}{\Delta}=\dfrac{1}{2}(1)(1)(\sin A)$ $\color{#D61F06}{\Delta}$ is max when $\sin A=1$ or $A=90°$ . Thus $\boxed{\textbf{the right isoceleles triangle}}$ will have the max area.

$\color{#D61F06}{\Delta_{\text{max}}}=\boxed{\dfrac{1}{2}}$

You always post the neatest solution! Kudos!!

Pi Han Goh - 5 years, 2 months ago

Rishabh Jain - 5 years, 2 months ago

Pi Han Goh - 5 years, 2 months ago

What About The Third Side?

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