Question

Diagonals of parallelograms

Find the length of VW.

Answer 1

VW = 30

VW = 5x -8

VW = 5(10) - 8

VW = 50-8

VW = 38 Not true as angles are congruent doesn't mean lengths are.

VW = 2x+10

VW = 2(10) + 10

VW = 20+10

VW = 30 True as section lengths to centre should be equal from different lengths with parallelograms.

VW = 2(6) +10 = 12+20 = 22 not true

VW = 5(6) - 8 = 30 - 8 = 22 not true.

Explanation:

2x + 10 = 3x

2x+10 -3x = 3x-3x

-1x +10 = 0

10/1 = 10

x = 10

2x+10 = 5x - 8

2x+10 -5x = 5x-5x -8

-3x +10 = -8

-3x+10+8 = -8+8

-3x+ 18

x = 18/3

x = 6

x = 10 as parallelograms have congruent diagonals angles.

Answer 2

The diagonal is divided equally:

YV = VW

`2x + 10 = 3x \\ \\ 3x - 2x = 10 \\ \\{ \underline{ x = 10}}`

VW = 3x

VW = 3(10)

VW = 30