Question

A quadrilateral is shown. One pair of opposite sides have lengths of 10 inches and (x + 2) inches. The other pair of opposite sides have lengths (x + 5) inches and (2 x minus 3) inches. Based on the measures shown, could the figure be a parallelogram? Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in. Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in. No, there are three different values for x when each expression is set equal to 10. No, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent

Answer 1

Answer: Choice A

Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in.

=============================================================

Step-by-step explanation:

Let's say the top and bottom sides are 10 inches and (x+2) inches.

If this was a parallelogram, then those opposite sides must be parallel and the same length. So x+2 = 10 which leads to x = 8 after subtracting 2 from both sides.

Now let's consider the other pair of opposite sides (x+5) and (2x-3), which would be the left and right sides. Set them equal to one another and solve for x.

x+5 = 2x-3

x-2x = -3-5

-x = -8

x = 8

We arrive at the same x value, which confirms we do have a parallelogram.

Use this x value to find the unknown sides

x+2 = 8+2 = 10

x+5 = 8+5 = 13

2x-3 = 2(8)-3 = 13

This parallelogram has sides of 10, 13, 10, 13

It might be helpful to think of a 10 by 13 rectangle. However, the parallelogram may or may not be a rectangle.