An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of $32$ and the triangle has an area of $16$ . What are the lengths of sides A and B?

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An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of $32$ and the triangle has an area of $16$ . What are the lengths of sides A and B?

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Answer 1 · 2017-11-13T21:10:46

$sqrt257~~16.03$

Explanation:

First things first - we start off with a diagram!
enter image source here
Not the most elegant diagram in the world, but it does the job. By convention, the side opposite angle $A$ is $a$ , opposite angle $B$ is $b$ and $C$ is $c$ . $h$ is the perpendicular bisector of AB at M - it cuts AB in half at a right angle.

Let $a=b=x$ . Our job is to find $x$ .

$Area_triangle=1/2bh$
$16=1/2xx32h$
$16=16h$
$h=1$

Now, we can apply Pythagoras' Theorem in one of the right-angled triangles. We have the height $h=1$ and the base $=16$ , so we can work out x.

$1^2+16^2=x^2$
$1+256=x^2$
$x^2=257$
$x=sqrt257~~16.03$

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An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of $32$ and the triangle has an area of $16$ . What are the lengths of sides A and B?

1 Answer

Explanation:

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Science

Math

Humanities

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An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of 32 32 and the triangle has an area of 16 16 . What are the lengths of sides A and B?

1 Answer

Explanation:

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An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of $32$ and the triangle has an area of $16$ . What are the lengths of sides A and B?