Mathematics
A rectangle of area 144 cm2 has its length equal to x cm. Write down its breadth in terms of x. Given that its perimeter is 52 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
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Answer
Given,
Area of rectangle = 144 cm2
Length = x cm
Perimeter = 52 cm
Area = length × breadth
⇒ 144 = x × breadth
⇒ Breadth = cm.
Perimeter = 2(l + b)
⇒ 52 = 2(x + )
⇒ x + = 26
⇒
⇒ x2 + 144 = 26x
⇒ x2 - 26x + 144 = 0
⇒ x2 - 18x - 8x + 144 = 0
⇒ x(x - 18) - 8(x - 18) = 0
⇒ (x - 18)(x - 8) = 0
⇒ x = 18 or x = 8
If x = 18 then,
Length = x = 18 cm.
Breadth = = 8 cm.
If x = 8 then,
Length = x = 8 cm.
Breadth = = 18 cm.
Generally we consider length > breadth
Hence, length = 18 cm and breadth = 8 cm.
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