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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

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

The length of the three sides of a triangle are 13cm, 14 cm, and 15cm. Find the length of the altitude to the 14-cm side.

To determine

To find:

Length of the altitude to the 14-cm side of a triangle.

Explanation

Given:

Lengths of three sides of a triangle are 13cm, 14 cm and 15 cm.

Calculation:

Let ABC be the triangle with three sides of length 13cm, 14 cm and 15 cm.

Let x be the length of CD.

Length of DB is

DB=CBCDDB=14x

Then,

Consider the right triangle ΔADC

By Pythagoras theorem,

AC2=x2+AD2152=x2+AD2AD2=225x2AD=225x2........(1)

In a right triangle ΔABD

By Pythagoras theorem,

AB2=AD2+(14x)2132=AD2+(14x)2AD2=169(14x)2AD=169(14x)2......

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