Basic College Mathematics (9th Edition)

Published by Pearson

Chapter 8 - Geometry - Review Exercises: 69

Answer

$x = 34$ ft $y = 30$ ft The perimeter of the larger triangle is $104$ ft.

Work Step by Step

1. Using the small triangle, find the ratios between the lengths a) Ratio between $20$ ft and $17$ ft (Large triangle: $40$ ft and $x$) $20a = 17$ $a = 0.85$ b) Ratio between $20$ ft and $15$ ft (Large triangle: $40$ ft and $y$) $20a = 15$ $a = 0.75$ 2. Use the ratios to find $x$ and $y$ a) Finding $x$ $x = 40 \times 0.85$ $x = 34$ ft b) Finding $y$ $y = 40 \times 0.75$ $y = 30$ ft Currently, the lengths in the large triangle are $30$ ft, $34$ ft and $40$ ft. 3. Find the perimeter of the large triangle Let $P =$ perimeter of the large triangle $P = 30 + 34 + 40$ $P = 64 + 40$ $P = 104$ ft Therefore the perimeter of the large triangle is $104$ ft.

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