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

3 is the proper answer

Answer 2

ANSWER


`x = 3`

`CD= 21 \: units`

`DE= 16 \: units`


`CE= 21 \: units`



Step-by-step 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 = (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`