Question

a scalene right triangle has a hypotenuse with a length of 50 cm. The length of one leg is twice the length of the other. What are the lengths of the legs of the triangle to the nearest tenth of a centimeter. Show your work.

Answer 1

Let
x------------> The length of one leg
y------------> The length of second leg

we know that
H=50 cm
x=2y
applying the Pythagorean theorem

H²=x²+y²--------> 50²=(2y)²+y²---------> 2500=4y²+y²-----> y²=2500/5
y=√500--------> y=22.4 cm
so
x=2y--------> x=2*22.4--------> x=44.8 cm

the answer is
the lengths of the legs of the triangle are
44.8 cm
and
22.4 cm