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प्रश्न
The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find the dimensions.
उत्तर
Let the breadth of rectangle be x cm.
According to the question:
Side of the square =`(x+4)cm`
Length of the rectangle=`{3(x+4)}` cm
It is given that the areas of the rectangle and square are same.
∴`3(x+4)xx x=(x+4)^2`
⇒`3x^2+12x=(x+4)^2`
⇒`3x^2+12x=x^2+8x+16`
⇒`2x^2+4x-16=0`
⇒`x^2+2x-8=0`
⇒`x^2+(4-2)x-8=0`
⇒`x^2+4x-2x-8=0`
⇒`x(x+4)-2(x+4)=0`
⇒`(x+4)(x-2)=0`
⇒`x=-4 or x=2`
∴ `x=2` ( ∵The value of x cannot be negative)
Thus, the breadth of the rectangle is 2 cm and length is `{3(2+4)=18}`
Also, the side of the square is 6 cm.
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