Answer:19cm and 12 cm
Explanation:
Let the length of the rectangle be x and width be y.
From the 1st condition,
The length of a rectangle exceeds the width by 5cm
i.e
x=y+5____(i)
From the 2nd condition,
If both were increased by 3cm the are would be increased by 96cm²
i.e
(x+3)(y+3)=xy+96 (here xy is the original area of the rectangle)
xy+3x+3y+9=xy+96
xy-xy+3x+3y=96-9 (canceling xy)
3(x+y)=87 (taking 3 common)
x+y=87/3 (changing the side of 3)
x+y=29_____(ii)
substituting the value of x in eqn(ii) from eqn(i)
x+y=29
y+5+y=29
2y=29-5
2y=24
y=24/2
y=12cm
Replacing the value of y in eqn(i)
x=y+5
x=12+5
x=19cm
The dimensions of the original rectangle are 19 cm and 12cm
Its my first time answering questions. Hope this helped.