In right triangle qrs, angle r is a right angle. The altitude rt is drawn to hypotenuse qs. If qr is 20 and qs is 25 then find the length of qt.

length of qt = 16

Step-by-step explanation:

Given in the question that qrs is a right angle triangle,

where qr = 20

sr = ?

qs = 25

qt = ?

1) Find sr

hypotenuse² = base² + height²

sq² = sr² + rq²

25² - 20² = sr²

sr = √25² - 20²

sr = 15

2)

When altitude rt is drawn to hypotenuse qs, it divides the triangle qrs into

two right angle triangle, rtq and rts.

Δrtq

height = rt

base = tq = 25 - x

hypotenuse = qt = 20

Δrts

height = rt

base = ts = x

hypotenuse = sr = 15

These both triangle shares same altitude that is rt

So, by using pythagorus theorem

Δ rtq Δ rts

hypotenuse² - base² = height² = hypotenuse² - base²

20² - (25 - x) ² = 15² - x²

400 - (625 + x² - 50x) = 225 - x²

400 - 625 - x² + 50x = 225 - x²

-225 - x² + 50x - 225 + x² = 0

-450 + 50 x = 0

50x = 450

x = 450/50

x = 9

base of Δ rtq = tq = 25 - x

tq = 25 - 9

tq = 16

The length of qt is 15

Step-by-step explanation:

According to Pythagorean Theorem

c² = a² + b²

c² - a² = b²

25² - 20² = b²

625 - 400 = b²

225 = b²

Taking square root on both sides

b = 15