Question

Two numbers are such that the ratio between them is 3:5 ,and its perimeter is 48m.Find the sides of a parallelogram.

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(p-q)^2 -(p+q)^2 = ?

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Answer 1

The answer is given below :

1 :

The ratio of two unequal sides of the parallelogram is 3 : 5

Let, the common multiple be x

Then, the two unequal sides are 3x m and 5x m

The perimeter of the parallelogram is

= 2 × (sum of two unequal sides)

= 2 × (3x + 5x) m

= 2 × 8x m

= 16x m

Given that,

perimeter of the parallelogram = 48 m

=> 16x = 48

=> x = 3

So, the two unparallel sides of the parallelogram are

3×3 m and 5×3 m

i.e., 9 m and 15 m

So, the four sides of the parallelogram are

9 m, 9 m, 15 m and 15 m.

2 :

Now,

${(p - q)}^{2} - {(p + q)}^{2} \\ \\ = ( {p}^{2} - 2pq + {q}^{2} ) - ( {p}^{2} + 2pq + {q}^{2} ) \\ \\ = {p}^{2} - 2pq + {q}^{2} - {p}^{2} - 2pq - {q}^{2} \\ \\ = - 4pq$

Thank you for your question, sister.

Answer 2

Hi friend
--------------
Your answer
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(1) Ratio of sides of a parallelogram = 3:5

Perimeter of the parallelogram = 48 m

Let the sides be 3x and 5x respectively.

Then,
----------

2(3x + 5x) = 48

=> 8x = 48/2

=> 8x = 24

=> x = 24/8

=> x = 3

Then
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Length of the parallelogram = 5x = (5 × 3) m = 15 m

Breadth of the parallelogram = 3x = (3 × 3) m = 9 m


(2) (p - q)² - (p + q)²

Using identity => (a² - b²) = (a + b)(a - b).

We get,
-----------

[(p - q) + (p + q)] [ (p - q) - (p + q)]

=> (p - q + p + q )(p - q - p - q)

=> 2p × (- 2q)

=> - 4pq

HOPE IT HELPS