Question

QRST is a parallelogram with diagonals (QS) ̅ and (RT) ̅ intersecting at point A. If (RT) ̅=x+15 and (RA) ̅=2x+3, what is the length of (RT) ̅? Show work to receive credit

Answer 1

The length of the diagonal of the parallelogram RT is 18 units.

Explanation:

RT=x+15

RA=2x+3

The point of intersection of the diagonals divides each one of the diagonal in to equal parts, then:

RA=TA=2x+3

RT=2 RA

Replacing RT by x+15 and RA by 2x+3 in the equation above:

x+15=2(2x+3)

Eliminating the parenheses applying the distributive property in the multiplication on the right side of the equation:

x+15=2(2x)+2(3)

Multiplying:

x+15=4x+6

Solving for x: Subtracting x and 6 both sides of the equation:

x+15-x-6=4x+6-x-6

Subtracting:

9=3x

Dividing both sides of the equation by 3:

9/3=3x/3

Dividing:

3=x

x=3

Replacing x by 3 in the equation:

RT=x+15

RT=3+15

RT=18