Chapter 5.6, Problem 42E

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Δ R S T , the altitudes of the triangle intersect at a point in the interior of the triangle. The lengths of the sides of Δ R S T are R S = 14 , S T = 15 , and T R = 13. a) If T X = 12 , find R X and X S . (HINT: Use the Pythagorean Theorem.)b) If R Y = 168 15 , find T Y and Y S . c) If S Z = 168 13 , find Z R and T Z . d) Use results from parts (a), (b), and (c) to show that R X X S ⋅ S Y Y T ⋅ T Z Z R = 1.

To determine

a)

To find:

RX and XS.

Explanation

Given:

In Î”RST, the altitudes of the triangle intersect at a point in the interior of the triangle. The lengths of the sides of Î”RST are RS=14,ST=15,TR=13 and TX=12.

Calculation:

From the figure, RTX is a right triangle.

By Pythagoras theorem, we get (RT)2=(RX)2+(TX)2.

(RT)2=(RX)2+(TX)2RX<

To determine

b)

To find:

TY and YS.

To determine

c)

To find:

ZR and TZ.

To determine

d)

To prove:

RXXSSYYTTZZR=1.

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