the length of the hypotenuse of a 45-45-90 triangle is 16 cm. what is the length of each leg

Answer 1

If you have a 45-45-90 triangle, the legs are the same length.

a2 + b² = c²

Since a = b...

2a² = 16²

2a² = 256

a² = 128

a = √128

a = 11.3 cm

Answer 2

In general, the lengths of the sides of a 45-45-90 triangle fit the pattern; where the length of the legs are equal and the hypotenuse is the length of the leg times the square root of 2.

x√2 = 16

Square both sides

x²(2) = 16²

2x² = 256

Just solve for x

You can also use the Pythagorean Theorem

A 45-45-90 Right Triangle sounds like a triangle with two equal angles and two equal sides.

Since the hypotenuse is 16

Then the Pythagorean Theorem

a² + b² = c²

Can be viewed as

a = b = x

x² + x² = c²

Plugging in the numbers

2x² = 16²

2x² = 256

x² = 256/2

x² = 128

x =√128

x = 8√2

You can plug this back into the Pythagorean Theorem to see if it works

You can check into the special relationship between the sides of a 45-45-90 degree Right Triangle online.

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