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? 1.Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in. 2.Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in. 3.No, there are three different values for x when each expression is set equal to 10. 4.No, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

Answer 1

Sides given by

• 10
• x+2
• x+5
• 2x+3

Opposite sides must be equal

Let's check once

`\\ \tt\hookrightarrow x+5=2x+3\implies x=2`

Find sides now

• 10in
• 2+2=4in
• 2+5=7in
• 2(2)+3=4+3=7in

One pair of opposite sides are equal but others not .

• It's a trapezium.

Answer 2

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

Explanation:

The opposite pairs are:

1)

• 10 in with x + 2 in
• It makes:
• x =+2 = 10 ⇒ x = 8 and both sides 10 in

2)

x + 5 with 2x - 3

It makes:

• 2x - 3 = x + 5
• 2x - x = 5 + 3
• x = 8

The sides are:

• 8 + 5 = 13 and
• 2*8 - 5 = 13 in

Correct answer choice is 1)