SOLUTION: if the length of the rectangle is reduced by 5 units and its breadth is increased by 3 units then the area of rectangle is reduced by 8 square units. if length is reduced by 3 uni
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Question 1096586: if the length of the rectangle is reduced by 5 units and its breadth is increased by 3 units then the area of rectangle is reduced by 8 square units. if length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 6 7 square units. Then find the length and breadth of the rectangle. Found 2 solutions by ankor@dixie-net.com, ikleyn:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! I am going to ignore the 7 in the last sentence
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Write an equation for each and reduce to a simple 2 unknown equation
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if the length of the rectangle is reduced by 5 units and its breadth is increased by 3 units then the area of rectangle is reduced by 8 square units.
(L-5)(w+3) = LW - 8
FOIL
LW + 3L - 5w - 15 = LW - 8
LW - LW + 3L - 5W = 15 - 8
3L - 5w = 7
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if length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 6 square units.]
(L-3)(w+2) = Lw + 6
Lw + 2L - 3w - 6 = Lw + 6
Lw - Lw + 2L - 3w = 6 + 6
2L - 3w = 12
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Using these two equations
3L + 5w = 7
2L - 3w = 12
multiply the 1st by 2 and the 2nd by 3
6L + 10w = 14
6L - 9w = 36
----------------subtraction eliminates L find w
0 - w = - 22
w = 22 units is the width
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Find the Length using the 1st equation
2L - 3(22) = 12
2L - 66 = 12
2L = 12 + 66
2L - 78
L = 78/2
L = 39 units is length
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Find the original area: 39 * 22 = 858 sq units
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see if this checks out in the statement:
" if the length of the rectangle is reduced by 5 units and its breadth is increased by 3 units then the area of rectangle is reduced by 8 square units.
(39-5) * (22+3) = 858 - 8
34 * 25 = 850
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You can check for yourself in the 2nd statement
