Question

Use the image to answer the question.

A parallelogram has vertices upper R, upper S, upper U, and upper T. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper V. The lines formed between each vertex and upper V are labeled.

Image Long DescriptionThe line connecting upper R to upper V is labeled 3 m plus 2. The line connecting upper S to upper V is labeled 2 n plus 2. The line connecting upper U to upper V is labeled 8 plus n. The line connecting upper T to upper V is labeled 4 m minus 3.

If quadrilateral RSTU
is a parallelogram, what are the lengths of the diagonals of the figure?

(1 point)
Diagonal RT
is equal to
and diagonal SU
is equal to
.

Answer 1

Because the diagonals bisect each other, RV = TV and SV = UV.

Set 3m + 2 = 4m − 3 → m = 5.
Set 2n + 2 = n + 8 → n = 6.

RV = 3(5)+2 = 17, so RT = 2·17 = 34.
SV = 2(6)+2 = 14, so SU = 2·14 = 28.

Answer: RT = 34, SU = 28.