Question

The difference in lenght between the two adjacent sides of a parallelogram is 5 cm. If the perimeter of the parallelogram is 58 cm, find the measure of all its sides​

Answer 1

Answer:

Two opposite parallel sides of 12 cm

Two opposite parallel sides of 17 cm

Step-by-step explanation:

In a parallelogram, opposite sides are parallel and equal in length.

If the difference between the two adjacent sides is 5cm,

then let one side = x

and the other side = x - 5

The perimeter is the distance around the shape, and we are told that the perimeter is 58 cm. So we can create an equation for the perimeter and solve for x:

  2x + 2(x - 5) = 58

⇒ 2x + 2x - 10 = 58

⇒ 4x - 10 = 58

⇒ 4x = 48

⇒ x = 48 ÷ 4

⇒ x = 12

Therefore, one adjacent side = 12 cm and the other adjacent side = 12 + 5 = 17 cm

Answer 2

the difference between the length of two adjacent sides is 5cm and the perimeter of the parallelogram is 58cm.

we know that opposite sides of a parallelogram are equal.

let one pair of opposite sides be x and another one y.

therefore x - y = 5cm (since they are adjacent sides

=> x = 5 + y

formula for the perimeter of a parallelogram is same as rectangle '2(l + b)'

=> 2(l + b) = 58cm

=> 2(5 + y + y) = 58cm

=> 5 + 2y = 58/2

=> 5 + 2y = 29

=> 2y = 29 - 5

=> 2y = 24cm

=> y = 24/2

=> y = 12cm

hence, the length of the adjacent sides are :-

y = 12cm

=> x - y = 5cm

=> x - 12 = 5cm

=> x = 5 + 12

=> x = 17cm

measure of all sides of the parallelogram are 12cm, 17cm, 12cm and 17cm. (since opposite sides are equal)



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