Question

part ii: parallelograms

1. find ml.

j 3x + 11 k
n 45 p
m 10x - 12 l

Explanation:

Step1: Use the mid - segment formula for trapezoids

In a trapezoid, the length of the mid - segment (NP) is given by the formula $NP=\frac{JK + ML}{2}$. We know that $JK = 3x+11$, $ML=10x - 12$ and $NP = 45$. So, $45=\frac{(3x + 11)+(10x - 12)}{2}$.

Step2: Simplify the right - hand side of the equation

First, simplify the numerator: $(3x + 11)+(10x - 12)=3x+10x+11 - 12=13x - 1$. The equation becomes $45=\frac{13x - 1}{2}$.

Step3: Solve for x

Multiply both sides of the equation by 2: $45\times2=13x - 1$, so $90 = 13x-1$. Add 1 to both sides: $90 + 1=13x$, which gives $91 = 13x$. Divide both sides by 13: $x=\frac{91}{13}=7$.

Step4: Find the length of ML

Substitute $x = 7$ into the expression for ML. $ML=10x - 12$. So, $ML=10\times7-12=70 - 12=58$.

Answer:

58