Question

1. $\triangle cde$ is an isosceles triangle with $overline{cd}congoverline{de}$. if $cd = 9x - 25$, $de = 6x + 8$, and $ce = 10x - 73$, find the value of $x$ and the measure of each side.

Explanation:

Step1: Set equal sides

Since $\overline{CD}\cong\overline{DE}$, we set $9x - 25=6x + 8$.
$9x-6x=8 + 25$
$3x=33$
$x = 11$

Step2: Find length of $CD$

Substitute $x = 11$ into the expression for $CD$: $CD=9x-25=9\times11-25=99 - 25=74$.

Step3: Find length of $DE$

Substitute $x = 11$ into the expression for $DE$: $DE=6x + 8=6\times11+8=66+8=74$.

Step4: Find length of $CE$

Substitute $x = 11$ into the expression for $CE$: $CE=10x-73=10\times11-73=110 - 73=37$.

Answer:

$x = 11$, $CD = 74$, $DE = 74$, $CE = 37$