Question

The altitude of a right triangle is 7 cm less than it's base . If the Hypotenuse is 13 cm . Find the other two sides.

Answer 1

HOPE IT WILL HELP YOU..... :-)

Answer 2

Let the base is x.
So, altitude = x - 7 cm.

By Pythagoras' theorem,

Hypotenuse^2 = Base^2 + Altitude^2

( 13 cm ) ^2 = x^2 + ( x - 7 cm )^2

169 cm^2 = x^2 + x^2 + 49 cm^2 - 14 cmx

169 cm^2 - 49 cm^2 = 2 x^2 - 14 cmx

120 cm^2 = 2 ( x^2 - 7 cmx )

x^2 - 7 cmx - 60 cm^2 = 0.

x^2 - 12 cmx + 5 cmx - 60 cm^2 =0

x ( x - 12 cm ) + 5 cm ( x - 12 cm ) = 0

( x - 12 cm ) ( x + 5 cm ) = 0

x = 12 cm or x = -5 cm ( It can't be as nothing can be measured negatively ).

Base = x = 12 cm.

Altitude = x - 7 cm = 12 cm - 7 cm = 5 cm.