Question

question 2 (multiple choice worth 1 points) (02.06r mc) isosceles trapezoid abcd is shown with midsegment ef. if base bc = 22x, base ad = 17x + 12, and ef = 18.5x + 8, what is bc? 22 37 44 58

Explanation:

Step1: Recall mid - segment formula

The formula for the length of the mid - segment of a trapezoid is $EF=\frac{BC + AD}{2}$.

Step2: Substitute given expressions

Substitute $BC = 22x$, $AD=17x + 12$, and $EF = 18.5x+8$ into the formula: $18.5x + 8=\frac{22x+(17x + 12)}{2}$.

Step3: Simplify the right - hand side

First, simplify the numerator of the right - hand side: $22x+(17x + 12)=39x + 12$. So the equation becomes $18.5x + 8=\frac{39x + 12}{2}$. Multiply both sides by 2 to get $2(18.5x + 8)=39x + 12$. Expand the left - hand side: $37x+16 = 39x + 12$.

Step4: Solve for x

Subtract $37x$ from both sides: $16=2x + 12$. Then subtract 12 from both sides: $4 = 2x$. Divide both sides by 2, we get $x = 2$.

Step5: Find BC

Since $BC = 22x$, substitute $x = 2$ into the expression for $BC$. So $BC=22\times2=44$.

Answer:

C. 44