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:-

Dimensions of the rectangle are 18cm [length] and 8cm [breadth] .

Explanation:-

We have :-

→ Area of the rectangle = 144 cm²

→ Length = x cm

→ Perimeter = 52 cm

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Let the assume that the breadth of the rectangle is 'b' cm.

Area of a rectangle = Length × Breadth

⇒ x × b = 144

⇒ b = 144/x

Hence, breadth in terms of 'x' is 144/x .

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Now :-

Perimeter of a rectangle :-

Perimeter of a rectangle :-= 2( Length + Breadth )

⇒ 2( x + 144/x ) = 52

⇒ 2x + 288/x = 52

⇒ 2x² + 288 = 52x

⇒ 2x² - 52x + 288 = 0

⇒ 2(x² - 26x + 144) = 0

⇒ 2(x² - 8x - 18x + 144) = 0

⇒2[x(x - 8) - 18(x - 8)] = 0

⇒ 2(x - 18)(x - 8) = 0

⇒ x = 18 ; x = 8

Answer 2

Answer:

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.