Question

Multiple ChoiceIf AC =3y + 13 and BD = 28 - 2y, find the value of y that makes thetrapezoid isosceles.

Answer 1

D) y = 3

Step-by-step explanation:

We were given that:

AC = 3y + 13

BD = 28 - 2y

From the diagram, for the figure to be an isosceles trapezoid, that would imply that diagonals AC & BD are congruent

`\begin{gathered} AC=BD \\ 3y+13=28-2y \\ \text{Put like terms together, we have:} \\ \text{Add ''2y'' to both sides, we have:} \\ 3y+2y+13=28 \\ 5y+13=28 \\ \text{Subtract ''13'' from both sides, we have:} \\ 5y=28-13 \\ 5y=15 \\ \text{Divide both sides by ''5'', we have:} \\ y=(15)/(5)=3 \\ y=3 \\ \\ \therefore y=3 \end{gathered}`

The value of "Y" that makes the diagram an isosceles trapezoid is: y = 3

Therefore, the correct option is D