Question

Originally a rectangle has dimensions 12in by 8in. If both are increased by the same amount, the area is doubled. Find the new dimensions. Hint x = the amount your are increasing each side by.
A.) 16 in by 12 in

B.) 14 in by 10 in

C.) 4 in by 48 in

D.) 8 in by 24 in

Answer 1

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

Answer 2

The answer would be A because it has to increase not decrease in x. 12*8=96. 2(96)=192
16*12=192 :)