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.​

Answer 1

Step-by-step explanation:

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 :-

= 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

Solution :

Given that:

Perimeter of rectangle = 44 cm

Area of rectangle = 105 cm2

Length of rectangle = x cm.

Now, perimeter of rectangle = 2 (length +

breadth) = 44

=> 2 (x + breadth) = 44

→ x + breadth = 22

→ breadth of the rectangle = 22 - x Again, area of rectangle = 105 cm2

length x breadth = 105 ⇒ xx (22-x) = 105

→ 22x - x2 = 105

→ x2 - 22x + 105 = 0

⇒ x2 - 15x - 7x + 105 = 0

(x-15)(x-7)= 0

⇒ x = 15 or 7

When x = 15, breadth of the rectangle =

22 x 22 - 15 = 7 cm

and when x = 7, breadth of the rectangle

= 22 - x = 22 - 7 = 15 cm

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