Question

A square has a side length of 3x meters. One of its sides is increased by 5 meters while the other side is decreased by 2 meters. The resulting figure is a rectangle. 1.What is the area of the rectangle in terms of x? 2.If x = 7 meters, what is the area of the rectangle?

Answer 1

Answer:

Let the length of the rectangle be x metres and the breadth be y metres.

Area of the rectangle=length×breadth

=x×y=xy sq. metres

From the given information, we have,

(x+3)×(y−4)=xy−67

and(x−1)×(y+4)=xy+89

(x+3)×(y−4)=xy−67

=>xy−4x+3y−12=xy−67

=>4x−3y=55

=>4x=3y+55....(i)

Also,(x−1)×(y+4)=xy+89

=>xy+4x−y−4=xy+89

=>4x−y=93....(ii)

Substituting equation (i) in equation (ii), we get,

4x−y=93

=>3y+55−y=93

=>2y=38

=>y=19

Substituting y=19 in equation (i), we get,

4x=3y+55

=>4x=3(19)+55

=>4x=112

=>x=28

Therefore, length of rectangle =x=28 metres

breadth of rectangle =y=19 metres

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