   Chapter 5.6, Problem 25E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

Given: R V → bisects ∠ S R T , R S = x − 6 , S V = 3 , R T = 2 − x , and V T = x + 2 Find: x (HINT: You will need to apply the Quadratic Formula.)

To determine

To find:

The value of x.

Explanation

Given:

RV bisects SRT, RS=x6,SV=3,RT=2x,VT=x+2.

Theorem used:

Angle bisector theorem:

If a ray bisects one angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the two sides that form the bisected angle.

Calculation:

We have RV bisects SRT.

By angle bisector theorem, we get

SRRT=SVVT.

Given that RS=x6,SV=3,RT=2x,VT=x+2

Thus x62x=3x+2.

Now let us find x.

x62x=3x+2(x6)(x+2)=3(2x)x2+2x6x12=63xx24x126+3x=0x2x18=0

Let us find the value of x using the quadratic formula, x=b±b24ac2a

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