If the length and breadth of a rectangle are increased by 3m and 2m,respectively the area would increase by 52
sq.m.If the length and breadth are decreased by 2m and 3m,respectively the area would decreased by 43sq.m.Find the length and breadth of the rectangle?
not bad
Putting all that into math, we have
(l+3)(b+2) = l*b+52
(l-2)(b-3) = l*b-43
Now just solve for l and b.
To solve this problem, we can set up a system of equations.
Let's denote the initial length of the rectangle as L and the initial breadth as B.
According to the problem, if we increase the length by 3m and the breadth by 2m, the area increases by 52 sq.m. This can be represented as:
(L + 3)(B + 2) = LB + 52 -- equation (1)
Similarly, if we decrease the length by 2m and the breadth by 3m, the area decreases by 43 sq.m. This can be represented as:
(L - 2)(B - 3) = LB - 43 -- equation (2)
Now, let's simplify the equations:
Expanding equation (1):
LB + 3B + 2L + 6 = LB + 52
3B + 2L = 46 -- equation (3)
Expanding equation (2):
LB - 2B - 3L + 6 = LB - 43
-2B - 3L = -49 -- equation (4)
Now, we have a system of equations (3) and (4) with two variables, B and L.
We can solve this system using any method, such as substitution or elimination. Let's use the substitution method:
From equation (3), we can isolate B:
B = (46 - 2L) / 3
Substituting this value of B into equation (4):
-2((46 - 2L) / 3) - 3L = -49
Simplifying and solving for L:
-92 + 4L - 9L = -147
-5L = -55
L = 11
Now, substituting this value of L into equation (3) to find B:
3B + 2(11) = 46
3B = 24
B = 8
Therefore, the length of the rectangle is 11m and the breadth is 8m.