Question

1. $\triangle mkl$ is an isosceles triangle with $overline{mk} cong overline{ml}$. if $mk = 7x - 15$, $kl = 4x - 5$, and $ml = 10x - 42$, find $x$ and the measure of each side.

Explanation:

Step1: Set up the equation

Since \(\overline{MK}\cong\overline{ML}\), we have \(7x - 15=10x - 42\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides:
\(-15 = 3x-42\).
Add \(42\) to both sides:
\(27 = 3x\).
Divide both sides by \(3\):
\(x = 9\).

Step3: Find the length of each side

For \(MK\): Substitute \(x = 9\) into \(MK=7x - 15\), \(MK=7\times9 - 15=63 - 15 = 48\).
For \(ML\): Substitute \(x = 9\) into \(ML = 10x - 42\), \(ML=10\times9 - 42=90 - 42 = 48\).
For \(KL\): Substitute \(x = 9\) into \(KL = 4x - 5\), \(KL=4\times9 - 5=36 - 5 = 31\).

Answer:

\(x = 9\), \(MK = 48\), \(ML = 48\), \(KL = 31\)