Question 8 X = Side CD = Side DE %3D Side CE = 14. ACDE is an sosceles triangle with CD = DE . If CD = 9x - 25, DE = 6x + 8, and CE = 10x - 73, find the value of x and the measure of each side. Blank 1: Blank 2: Blank 3: Blank 4:

Question 8 X = Side CD = Side DE %3D Side CE = 14. ACDE is an sosceles triangle with CD = DE . If CD = 9x - 25, DE = 6x + 8, and CE = 10x - 73, find the value of x and the measure of each side. Blank 1: Blank 2: Blank 3: Blank 4:

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter7: Triangles

Section7.3: The Ambiguous Case

Problem 46PS

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Question

Expert Solution

Step 1

Given $△ C D E$ is an isosceles triangle with $\bar{C D} = \bar{D E}$ .

Also, given that $C D = 9 x - 25, D E = 6 x + 8$ and $C E = 10 x - 73$ .

To find the value of $x$ and the measure of each side.

Solution:

We know that isosceles is a triangle in which any two sides are equal.

Here, we have given $\bar{C D} = \bar{D E}$ .

Therefore,

$\begin{array}{rcl} \bar{C D} & = & \bar{D E} \\ 9 x - 25 & = & 6 x + 8 \\ 9 x - 6 x & = & 8 + 25 \\ 3 x & = & 33 \\ x & = & \frac{33}{3} \\ x & = & 11 \end{array}$

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