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
Algebra.Com
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
:
Write an equation for each and reduce to a simple 2 unknown equation
:
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
:
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
:
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
:
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
:
:
Find the original area: 39 * 22 = 858 sq units
:
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
:
:
You can check for yourself in the 2nd statement
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
". . . then the area of rectangle will increase by 6 7 square units."
By how much units ? ? ? ? ? ?
Could you write it more accurately please ? Thanks.
RELATED QUESTIONS
If the length of a given rectangle is increased by 3 inches and the breadth is reduced by (answered by josgarithmetic)
The area of a rectangle gets reduced by 8 sq. metre, if its length is reduced by 5 metre... (answered by lwsshak3)
Length of a rectangle is greater than its breadth by 3 CM if the length is increased by 9 (answered by josgarithmetic)
Length of a rectangle is 5 cm less then twice its breadth, if the length is decreased by... (answered by ankor@dixie-net.com)
perimeter of a rectangle is 66 units when length and breadth are increased by 7 units... (answered by ankor@dixie-net.com)
If in a rectangle, the length is increaded and the breadth is reduced by 2 units each,... (answered by josgarithmetic)
If the length of a rectangle is increased by 40% and the breadth is reduced by 20%, what... (answered by math_helper,rothauserc,MathTherapy)
The length of a rectangle exceed its width by 6 units. If each dimension is increased by... (answered by richwmiller)
If the length of the rectangle is exceeds its breadth by 7cm and the length is decreased... (answered by josgarithmetic)