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word problem

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by dikku07 » Wed May 20, 2009 10:09 am
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and the breadth is increased by 3 units. if we increase the length by 3 units and the breadth by 2 units, then the area is increased by 67 square units. Find the length and breadth of the rectangle.
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by Katrusya » Wed May 20, 2009 10:33 am
L-lenght, B-breath
According to the question, create the equations
(B*L-9)=(L-5)(B+3) - first situation
(B*L+67)=(L+3)(B+2) - second situation

Solve the equations and you'll get:
L=17
B=9
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Re: word problem

by kvamsy » Wed May 20, 2009 10:37 am
L = 17 , B = 9

by solving two equations

1) 3l-5b = 6
2) 2l-3b = 61
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by raleigh » Wed May 20, 2009 10:39 am
Let A be the area of the rect., l be the length of the rect., and w be the width of the rect. Then l * w = A. We will reference this by .

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and the breadth is increased by 3 units gives us:

(l-5)(w+3) = A - 9 We will reference this by [ii]

If we increase the length by 3 units and the breadth by 2 units, then the area is increased by 67 square units gives us

(l+3)(w+2) = A + 67 We will reference this by [iii]

Expand [ii]:
lw + 3l -5w -15 = A - 9
Substitute A for lw by and simplify.
[ii] becomes 3l - 5w = 6

Expand [iii]:
lw + 2l + 3w + 6 = A + 67
Substitute A for lw by and simplify.
[iii] becomes 2l + 3w = 61

Now solve the system of equations
3l - 5w = 6
2l + 3w = 61
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by dikku07 » Wed May 20, 2009 10:43 am
thanks. i had unnecessary complicated the problem by taking area as unknown a instead of l x b
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