Question

Write an equation and solve for X if the area of the rectangle is 70 square units
(Describing the rectangle)

X + 4 at the top and 7 on the left side

Answer 1

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In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle.

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Solution

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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