CDE is an isosceles triangle with D equal to E. If CD= 4x+9, DE= 7x-5 and CE=16x-27, find the x and the measure of each side

Question

CDE is an isosceles triangle with D equal to E. If CD= 4x+9, DE= 7x-5 and CE=16x-27, find the x and the measure of each side

x =

CD =

DE =

CE =

Answer 1

By definition, an isosceles triangle has two congruent angles and two congruent sides. The congruent sides are opposite the congruent angles. We are told angles D and E are equal, so CE ≅ CD.

CE = CD

16x - 27 = 4x + 9

12x = 36

x = 3

CD =4x + 9

=4(3) + 9

=12 + 9

=21

DE = 7x - 5

=7(3) - 5

=21 - 5

=16

x=3

CE = 21

CD = 21

DE = 16

Answer 2

CDE=αβγ (angles)

opposite

abc (sides)

D=E=β=γ

c=4x+9

a=16x-27

2β+γ=180

or

2α+γ=180

(a^2+c^2-2ac*cosβ)=b^2

Substitute