Question

the length of a rectangle exceeds it's width by 5m if the width is increased by 1 m and the length is decreased by 2 m the area of the new triangle is 4sq. m less than the area of the original rectangle find the dimensions of the original rectangle

Answer 1

let length of rectangle =x and width =y
now according to question
x=y+5
area of rectangle=xy=(y+5) y
again length =x-2 and width=y+1
now area of rectangle=(x-2)(y+1)
again question ask

(x-2)(y+1)=y (y+5)-4
(y+5-2)(y+1)=y (y+5)-4
(y+3)(y+1)=y^2+5y-4
y^2+4y+3=y^2+5y-4
y=7
and x=y+5=12

Answer 2

The area is A = LW for a rectangle.
We have originally
L = W + 5
Then the area is (W+5)W = W^2 + 5W
(L-2)(W+1) = W^2 + 5W - 4
Substituting we get
(W+5 - 2)(W+1) = W^2 + 5W - 4
(W + 3)(W + 1) = W^2 + 5W - 4
W^2 + 4W + 3 = W^2 + 5W - 4
and W = 7 m so that
L = 12 m