Question

a rectangle of area 144 CM square has its length equal to X centimetre write down its breadth in term of X given that its perimeter is 52 centimetre write down an equation in x and solve it to determine the dimension of the rectangle

Answer 1

Step-by-step explanation:

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 × breadth = 105

⇒ x × (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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