# Find the length of the leg of the triangle 45-45-90 with a long hypotenuse of 25 inches.

Question
Find the length of the leg of the triangle 45-45-90 with a long hypotenuse of 25 inches.

2021-02-25
In a 45°-90°90° triangle, the length of the hypotenuse is 2–sqrt2 times each leg.
If x is the leg length, then we can write:
$$25=\sqrt{2\times x}$$
$$\frac{25}{\sqrt 2}= x$$
$$\frac{25}{\sqrt 2}\times \frac{\sqrt 2}{\sqrt 2}$$
$$x=\frac{(25\times \sqrt2)}{2}$$

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