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# The hypotenuse of an isosceles right triangle is $14\sqrt 2$. How long is each leg of the triangle?

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1. The hypotenuse of an isosceles right triangle is 14sqrt(2). How long is each leg of the triangle?

2.  The hypotenuse of an isosceles right triangle is 14sqrt(2). What is the area of the triangle?

Mar 23, 2021
edited by weredumbmaster22  Mar 23, 2021

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Both questions use the same triangle:

Note that an isosceles right triangle is a 1-1-sqrt(2) triangle;

meaning that we can find the legs by dividing the hypotenuse by sqrt(2).

$$14{\sqrt {2}}{\div }{\sqrt {2}}=14$$

1. The leg of the triangle is 14 units long.

The area is simply bh/2, where b=14 and h=14.

$${\frac {bh} {2}}={\frac {14{\times }14} {2}}=98$$

2. The area of the triangle is 98 square units.

Mar 23, 2021