A manufacturer makes rectangular table tops measuring 30 by 36 he wishes to make a table top that has 3 times the area by adding the same number to both length

Question

& width. Find the dimensions of the table tops he should manufacture. 

 

 

That is the rest of my question!

Answer 1

Initial area = 1080 square units; three times this area is 3240 square units. The new dimensions will be (30+X) and (36 + X) and the new area will generate the following equation (30 +X)* (36+X) = 3240. This will lead us to the following equation: X^2 + 66X +1080  = 3240 => X^2 + 66X -2160  = 0. solving for the quadratic equation we obtain x1 =24  and the other will be X2 = - 90 , not possible. the new dimensions of the tabletops will be:54   units by 60  units. 

Answer 2

A=30x36=1080 sq units

3x1080=3240 sq units

(x+36)(x+30)=3240

x²+66+1080=3240

x²+66x+1080-3240=0

x²+66x-2160=0

2160=2x2x2x2x3x3x3x5

90x24=2160

90-24=66

(x+90)(x-24)=0

x-24=0

x=24

check:30+24=54, 36+24=60, 60x54=3240 which is 3x1080

add 24 to both measurements to get 54 and 60