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: A =Yes, one pair of opposite sides could measure

10 in., and the other pair could measure 13 in.

Step-by-step explanation: jus to make it more simplier

Answer 2

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

Explanation:

we know that

A parallelogram have opposite sides parallel and congruent

so

If the given quadrilateral is a parallelogram

then

`10=x+2` ----> equation A

and

`x+5=2x-3` ----> equation B

solve equation A

`x=10-2=8\ in`

solve equation B

`2x-x=5+3\\x=8\ in`

The value of x is the same in both equations

That means

For x=8 inches opposite side are congruent

therefore

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