The square of the hypothenuse of a right-angled isoceles triangle is 128 m.Find the length of the sides.

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Solution

Since the the triangle is an isoceles triangle, then the two sides other than the hypotenuse will be equal.
Let us assume that one of the equal sides of the isoceles triangle be x m, then the other side will also be x m.
As per pythogoras theorom,
Hypotenuse² = Perpendicular² + Base²
( where Hypotenuse² = 128 m and Perpendicular = Base = x m.)
128 = x² + x²
2x² = 128
x² = 128/2 =64
x = √64 = 8m.
Ans: 8 m.

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