Question

The hypotenuse of a right triangle is 10 cm long. One of the triangle’s legs is 3

times the length of the other leg. Find the lengths of the two legs of the
triangle. Round to the nearest tenth if necessary

Answer 1

one side is
`√(10)` and other 3
`√(10)`

in decimal one side = 3.16

other side = 9.48

Explanation:

In right angle

if two sides containing right angle is a and b and h is hypotenuse then

by Pythagoras theorem

a^2 + b^2 = h^2

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let one side be x

given

One of the triangle’s legs is 3 times the length of the other leg

then other leg = 3x

given h = 10 cm

applying Pythagoras theorem

`a^2 + b^2 = h^2\\x^2 + (3x)^2 = 10^2\\x^2 + 9x^2 = 100\\10x^2 = 100\\x^2 = 100/10 = 10\\x = √(10)`

Thus, one side is
`√(10)` and other 3
`√(10)`

`√(10) = 3.16\\`

thus, in decimal one side = 3.16

other side = 3.16*3 = 9.48