Help finding lengths of triangle, please!

In a right triangle, a=90°, the hypotenuse is 8cm longer than one side and the other side is half the length of the hypotenuse.

Find the lengths of all sides. Can you please show the steps too! thankss ^_^

Try drawing out a right triangle.

so you have the variable x.

on the hypothenouse label 8+x (because the hypotenuse is 8 cm longer than one side)

and "the other side is half the length of the hypotenuse" (so one side is 0.5(8+x))

and the other side is just x.

solve in term of x

it's a right triangle so you know that
a^2 + b^2 = c^2.
c being the hypotenuse, and a and b being the regular sides.


so x² + 0.5(8+x)² = (8+x)²

now solve in term of x ((:
x = 19.3137 [i just solved it using wolfram alpha]

know go back to the original equation and plug 19.3137 in for x.

8+x --> 8+(19.3137). this is the hypotenuse
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solve the rest