Question

if the length of a rectangle is increased by 8m and the breath by 3m its area will be increased by 200m². Its length is increased by 3m and breath is increased by 8m, it's area will be increased by 255m². Find the length and breath of the rectangle.

Answer 1

First of all, let us suppose that the length, breadth and area of the original rectangle be L, B and A, respectively.

We know that, A = L × B -- equation 1

According to first statement of the question,

(L+8) × (B+3) = A+200
On simplifying this we get,
LB +8B+3L+24=A+200
(From equation 1, we have A=LB. Hence we will substitute that here.)
LB +8B+3L+24=LB+200
8B+3L=176 __equation 2

Similarly, according to the second statement of the question we have,

(L+3) × (B+8) = A+255
On simplifying we get,
3B + 8L = 231 __ equation 3

Now we just jave to solve equation 2 and 3.
for that multiply equation 2 with 3 and equation 3 with 8.
3 × (8B+3L=176)
8 × (3B+8L =231)

24B + 9L = 176×3
24B + 64L = 231×8
- - -
_______________
-55L = 528-1848= -1320
-55L = -1320
L = -1320/-55 = 24
L = 24 m
Now you can substitute the value of L obtained from here to any of the equations 2 or 3 and obtain the value of B.
Hence, substituting the value of L in equation 2, we get,

3B + 8L = 231
3B + 8×24 = 231
3B + 192=231
3B = 231 -192 =39
B = 39/3
B = 13 m
Now area of the original rectangle is,
A = LB = 24× 13 =312 m²

Hence we have got,
L = 24 m
B = 13 m
A = 312 m²