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julsineya
1 month ago
6

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 t

he length of qt.
Mathematics
2 answers:
lawyer [12.5K]1 month ago
5 0

Answer:

qt's length = 16

Step-by-step explanation:

The problem states that qrs is a right triangle,

where qr = 20

          sr =?

          qs = 25

          qt =?

1)

Calculate sr

hypotenuse² = base² + height²

sq² = sr² + rq²

25² - 20² = sr²

sr = √(25² - 20²)

sr = 15

2)

When altitude rt is dropped to hypotenuse qs, it creates

two right triangles: rtq and rts.

Δrtq

height = rt

base= tq = 25 - x

hypotenuse = qt = 20

Δrts

height = rt

base= ts = x

hypotenuse = sr = 15

Both triangles share the same height, which is rt

Using the Pythagorean theorem:

      Δ rtq                                           Δ rts

hypotenuse² - base² = height²

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  

Svet_ta [12.7K]1 month ago
3 0

Answer:

The length of qt is 15

Step-by-step explanation:

Referring to the Pythagorean Theorem:

c² = a² + b²

c² - a² = b²

25² - 20² = b²

625 - 400 = b²

225 = b²

Taking the square root gives us:

b = 15

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