Question

The height of a right triangle is 7cm less than it's base. If the hypotenuse is 13cm,then find out the base and height.

Answer 1

Let height of triangle be x
So base of the triangle will be x+7
Hypotenuse is 13 cm




Now by Pythagoras theorem
${(hypotenuse)}^{2} = {(base)}^{2} + {(height)}^{2}$
${13}^{2} = {(x + 7)}^{2} + {x}^{2} \\ 169 = {x}^{2} + 14x + 49 + {x}^{2} \\ 2 {x}^{2} + 14x - 120 = 0 \\ \\ divide \: \: both \: \: sides \: \: by \: \: \: 2 \\ {x}^{2} + 7x - 60 = 0 \\ {x}^{2} + 12x - 5x - 60 = 0 \\ x(x + 12) - 5( x + 12) = 0 \\ (x - 5)(x + 12) = 0$
Hence
x=5. or. x=-12

But side can't be negative
Hence height of triangle is 5 cm
and base is
x+7
=5+7
=12cm