The altitude corresponding to the side PQ and PS of a parallelogram PQRS is 36 cm and 40 cm respectively.Find the perimeter of the parallelogram for which area is given 180 cm square.
Answers
The perimeter of the parallelogram for which area is given 180 cm square is 19 cm.
Step-by-step explanation:
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
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Answer:
Step-by-step explanation:
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