Question

The altitudes corresponding to sides PQ and PS of a parallelogram PQRS are 36 cm and 40 cm respectively. Find the perimeter
of the parallelogram if its area is 180 cm2

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Answer 1

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Answer 2

Answer:

Required Formula:

(1) Area of parallelogram = base * height

(2) Perimeter of parallelogram = sum of lengths of all four sides  

Referring to the figure attached below, we have

ST = 36 cm [altitude corresponding to side PQ]

QU = 40 cm [altitude corresponding to side PS]

Area of the parallelogram PQRS = 180 sq. cm

Considering the altitude ST corresponding to side PQ, we get

The area of parallelogram = PQ * ST

⇒ 180 = PQ * 36

⇒ PQ = 180 / 36

⇒ PQ = 5 cm …… (i)

Now, considering the altitude QU corresponding to side PS, we get

The area of parallelogram = PS * QU

⇒ 180 = PS * 40

⇒ PS = 180 / 40

⇒ PS = 4.5 cm …… (ii)

Thus,  

The perimeter of the parallelogram PQRS,

= PQ + QR + RS + PS  

[Since opposite sides of parallelogram are equal in length, so PQ = RS & QR = PS ]

= 2 [PQ + PS]

= 2 * [5+4.5]

= 2 * 9.5

= 19 cm

Step-by-step explanation:

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