Question

10. In a parallelogram ABCD, AB = (x + 7) cm
and CD = (2x – 5) cm. Find AB.​

Answer 1

The length of side AB is 19 cm.

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Let's understand a few concepts:

To solve the given problem we will first take a look at the following properties of a parallelogram:

• Opposite sides of a parallelogram are parallel.
• Opposite sides are congruent.
• Opposite angles of a parallelogram are congruent.
• Diagonals of a parallelogram bisect each other.
• Consecutive angles of a parallelogram are supplementary.

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Let's solve the given problem:

Here we have,

ABCD is a parallelogram

The length of side AB = (x + 7) cm

The length of side CD = (2x - 5) cm

By using one of the above properties of a parallelogram i.e., the opposite sides of a parallelogram are congruent, we can form an equation as,

$(x + 7) = (2x - 5)$

$\implies 2x - x = 7 + 5$

$\implies \bold{x = 12}$

∴ $\bold{AB }= x + 7 = 12 + 7 = \bold{19\:cm}$

Thus, the length of side AB is 19 cm.

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Answer 2

Answer:

answer is 19 as

Step-by-step explanation:

ABCD is a parallelogram

the length of ab is (x+7)

the length of cd is (2x-5)

(x+7) = (2x-5)

7+5 = 2x - 1x

12 = x

therefore ab is

12 +7 =19 ( x + 7 )