Answer with Step-by-step explanation:
Originally a rectangle has dimensions 12 inch by 8 inch
Length=12 in.
Breath=8 in.
Original Area=12×8
= 96 in.²
x = the amount your are increasing each side by.
New length=(12+x) in.
New breath=(8+x) in.
New Area=(12+x)(8+x) in.²
If both are increased by the same amount, the area is doubled.
New Area=2×96=192 in.²
⇒ (12+x)(8+x)=192
⇒ 12(8+x)+x(8+x)=192
⇒ 96+12x+8x+x²=192
⇒ x²+20x-96=0
⇒ x²+24x-4x-96=0
⇒ x(x+24)-4(x+24)=0
⇒ (x+24)(x-4)=0
⇒ x= -24 or x= 4
But x can't be equal to -24 otherwise new length and breath will be negative which is not possible
Hence, Value of x is:
4
New length=(12+4) in.=16 in.
New breath=(8+4) in.=12 in.
Hence, new dimensions are:
A.) 16 in by 12 in
