Question

A rectangle of area 144cm.square has its length equal to x cm. Write down its breadth in terms of x. Given that its perimeter is 52cm, write down an equation in x and solve it to determine the dimensions of rectangle.

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Answer 1

Answer:

Case i

Breadth in terms of x=144/x cm

Case ii

Equation :- 2x+288/x=52

Case iii

Dimesions :length =18cm, breadth =8cm

Step-by-step explanation:

Case i

Area of rectangle(A) =length(L) × breadth(B)

144=x ×B

:-B=144/x cm

Case ii

Perimeter (P) =2(Length + breadth)

52=2(x + 144/x)

52=2x + 288/x

:-, 2x+288/x=52

Case iii

2x + 288/x=52

2x² + 288/x=52

2x² + 288=52x

2x² - 52x + 288=0(solve the quadratic equation)

We get, x=18 or x=8

:- Length =x cm=18cm

Breadth=144/x cm=144/18=8cm

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Answer 2

Answer:

L = B+6 …(1)

L+B = 60/2 = 30, or

L = 30-B …(2)

Equate (1) and (2)

B+6 = 30-B, or

2B = 24, or B = 12 so L = 18 cm.

The length = 18 cm, breadth = 12 cm and the area = 216 sq cm. ꉣ꒒ꁴ ꊰꄲ꒒꒒ꄲꅐ ꂵꏂ