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# what is the hypotenuse of a triangle 15/16 X 15/16

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what is the hypotenuse of a right angle triangle where the 2 sides are 15/16 and 15/16

Guest Sep 7, 2017
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#1
+4480
+2

The two legs must be  15/16  and  15/16  .

We can use the Pythagorean theorem to find the hypotenuse, which says....

(hypotenuse)2  =  (leg)2 + (other leg)2

Plug in  15/16  for the legs.

(hypotenuse)2  =  (15/16)2 + (15/16)2

Multiply out the exponents.

(hypotenuse)2  =  225 / 256 + 225/256

(hypotenuse)2  =  450 / 256

Take the positive square root of both sides.

hypotenuse  =  √( 450 / 256 )

hypotenuse  =  √450 / √256

hypotenuse  =  15√2 / 16      ≈  1.326

hectictar  Sep 7, 2017
#2
+1107
+1

We could make this problem easier computationally once we realize that this triangle must be an isosceles right triangle. An isosceles triangle happens to be a 45-45-90 triangle, a triangle that happens to be apart of the "special right triangles" category.

In a 45-45-90 triangle, know the ratio of the side lengths are $$1:1:\sqrt{2}$$. Now, let's solve for the hypotenuse.

 $$\frac{\frac{15}{16}}{1}=\frac{\text{hypotenuse}}{\sqrt{2}}$$ multiply by the square root of 2 on both sides. $$\frac{15}{16}\sqrt{2}=\text{hypotenuse}$$

As you'll notice, this is the exact answer that hecticar got. I ust used a different method.

TheXSquaredFactor  Sep 7, 2017

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