How to find the perimeter of an acute / obtuse triangle - GRE Quantitative Reasoning

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Question

The obtuse Isosceles triangle shown above has two sides with length and one side length . The length of side $\small a=$ $\small 9$ . The length of side $\small b=3a$ . Find the perimeter of the triangle.

Answer

To solve this problem, apply the formula: $\small p=2a+b$

Side $\small a=9$ , side $\small b$ must equal $\small 9\times3=27$

Since this is an Isosceles triangle, there must be two sides with a length of $\small 9$ .

Thus, plug in each side lengths value to find the solution:

$\small p=\small \small 9+9+(9\times 3)=9+9+27=45$

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