Answer:
The additional length is 3 ft
The new length of the rectangle after the increase is 15 ft and the width 13 ft
Explanation:
The area A of a rectangle is given as
A = L * B
where L is the length of the rectangle and B is the width
As such for a rectangle 10 ft by 12 ft, the area
= 10 * 12
= 120 sq ft
If this is increased by 75 sq ft, the new area becomes
= 120 + 75
= 195 sq ft
If the length and the width are to be increased by the same amount, let this amount be x then the new length will be 12 + x and width 10 + x such that
(12 + x)(10 + x ) = 195
expand
x² + 22x + 120 = 195
x² + 22x +120 - 195 = 0
x² + 22x - 75 = 0
x² +25x -3x - 75 = 0
x(x +25) -3(x + 25) = 0
(x + 25) (x- 3) = 0
x = -25 or 3
since the additional length cannot be negative, it is 3ft.
As such the new length
= 3 + 12 = 15 ft
the new width
= 10 + 3
= 13 ft