Chapter 5.2, Problem 39E

### 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

# For Exercises 39 to 40, use intuition to from a proportion based on the drawing shown. △ A B C has an inscribed rhombus A R S T . If A B = 10 and A C = 6 , find the length x of each side of the rhombus.

To determine

To calculate:

The length x of each side of the rhombus.

Explanation

Approach:

If C is a point of XYÂ¯ and Xâˆ’Câˆ’Y, then XC+CY=XY.

Rhombus:

It is a parallelogram with two congruent adjacent sides.

Similarity between Two polygons:

Two polygons are similar if and only if when all pairs of corresponding angles are congruent and all pairs of corresponding sides are proportional.

Given:

Î”ABC has an inscribed rhombus ARST. If AB=10 and AC=6.

Calculation:

According to the segment-Addition Postulate, AR+RB=AB.

It is given that AR=x,AB=10Â andÂ AC=6.

Substitute the value of ARÂ andÂ AB in an equation AR+RB=AB, we get

x+RB=10RB=10âˆ’x

According to the property of rhombus ARST, we can say that RS=AT

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