Question

Triangle CDE is an isosceles triangle with angle d congruent to angle E if CD= 4x+9, DE= 7x-5, CE= 16x-27, find x and the measure of each side.

Answer 1

ANSWER

$x = 3$
$CD= 21 \: units$
$DE= 16 \: units$

$CE= 21 \: units$



EXPLANATION

It was given that ∆CDE is an isosceles triangle.

The length of the sides are given in terms of x as follows.

$CD=4x+9$


$DE=7x-5$


$CE=16x-27$



It was also given that, angle D is congruent to angle E.


This implies that, side CD and CE are equal.


Thus,

$|CD| = |CE|$
In terms of x, we have;

$4x + 9 = 16x - 27$


We group like terms to get,

$16x - 4x = 9 + 27$

$12x = 36$

Divide both sides by 12 to get,

$x = \frac{36}{12}$

$\therefore \: x = 3$


The length of the sides are;

$CD=4(3)+9 = 21 \: units$

$DE=7(3)-5 = 16 \: units$


$CE=16(3)-27 = 21 \: units$