Question

In the parallelogram below, AB=2x+8 and CD=5x-1. Explain how you would find the length of AB?

Answer 1

Answer:

31:35

Step-by-step explanation:

2x−y=−4 (1)

And 3x−y=9 (2)

we will get x=13 and y=30

AB=2x+5=2(13)+5=31

And BC=3x−4=3(13)−4=35

AB:BC=31:35

Answer 2

Given:

In the parallelogram below, AB = 2x + 8 and CD = 5x - 1. Explain how you would find the length of AB?

To find:

Explain how you would find the length of AB?

Solution:

Let's say,

ABCD is the parallelogram

AB = 2x + 8 (given)

CD = 5x -1 (given)

From one of the properties of a parallelogram, we know that

$\boxed{\bold{Opposite\:sides\:are\:congruent\:i.e., \:equal \:in\:length}}$

Here the given sides AB and CD are the two opposite sides of the parallelogram ABCD, therefore, we can form the equation as,

length of AB = length of CD

on substituting the given values of AB and CD, we get

$\implies 2x + 8 = 5x - 1$

$\implies 5x - 2x = 8 + 1$

$\implies 3x = 9$

$\implies \bold{x = 3}$

∴ AB = 2x + 8 = (2 × 3) + 8 = 6 + 8 = 14

Thus, the length of AB is → 14 units.

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