# IB exams The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?

2
by devrajMand

2015-05-03T17:54:08+05:30
Let the breadth of the given rectangle be x then length is 2x.
thus area of the given rect is 2x^2

after dec 5cm from length and inc 5cm breadth
new lenght becomes 2x-5
thus new area =(2x-5)(x+5)
=2x^2-5x+10x-25
=2x^2+5x-25
since new area is 75 units greater than original area thus
2x^2+75=2x^2+5x-25
5x=75+25
5x=100
therefore x=20
hence length of the rectangle is 40 cm.
2015-05-03T18:20:29+05:30

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Rectangle  length = L and  breadth = B.
L = 2 B      and Area = LB = 2 B²

new length L' = L - 5 cm  = 2 B - 5  cm
new breadth  B' = B + 5 cm

New Area of rectangle = L'  B'
= (2B - 5) (B + 5)
=  2 B² + 10 B - 5 B  - 25

Increase in the  area =  L'B' - L B = 5 B - 25
= 75 cm²

=>  B = (75+25)/5    =  20 cm
=>     L = 2 B = 40 cm