cde is an isosceles triangle with d=e. if cd=4x+9, de=7x-5, and ce=16x-27, find x and the measure of each side.

Question

cde is an isosceles triangle with d=e. if cd=4x+9, de=7x-5, and ce=16x-27, find x and the measure of each side.

x=

cd=

de=

ce

Answer 1

Since d=e, we know that cd = ce.

Since cd=4x+9 and ce=16x-27, we know that 4x + 9 = 16x - 27

So 9 + 27 = 16x - 4x

And 36 = 12x

So x=3.

If x=3,

cd = 4x + 9 = 4(3) + 9 = 12 + 9 = 21

de = 7x - 5 = 7(3) - 5 = 21 - 5 = 16

ce = 16x - 27 = 16(3) - 27 = 48 - 27 = 21

So x=3, cd=21, de=16 and ce=21.