Answer:
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 = ?
<h3>1)</h3><h3>Find sr</h3>
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
