Question

ARST shown below, altitude SU is drawn to RT at U.If SU = h, UT=4, and RT-20, which value of h will make ARST a right triangle with LRST as a right angle?

Answer 1

we have that

If triangle RST is a right triangle and angle mthen

triangle SUT is a right triangle too

so

In the right triangle SUT

Applying the Pythagorean Theorem

ST^2=h^2+4^2 -------> equation A

In the right triangle RSU

Applying the Pythagorean Theorem

RS^2=h^2+16^2 -----> equation B

In the right triangle RST

Applying the Pythagorean Theorem

20^2=RS^2+ST^2 -------> equation C

substitute equation A and equation B in equation C

20^2=h^2+16^2+h^2+4^2

solve for h^2

400=2h^2+272

2h^2=128

h^2=64

h=8

answer is option 1