Question

Matt's rectangular patio measures 9 feet by 12 feet. he wants to increase the patio's dimensions so its area will be twice the area it is now. he plans to increase both the length and the width by the same amount, x. find x, to the nearest hundredth of a foot.

Answer 1

The present dimensions are : length = 12 feet

width = 9 feet

Area = 12* 9 = 108 feet squared

If the dimensions are increased by x feet the dimensions are :

length = 12 + x

width = 9+ x

Area = ( 12+x)( 9+x)

new area = initial area * 2

( 12+ x)( 9+ x) = 2 * 108

12*9 + 12x + 9x + xx = 216

108 + 21 x + x^2 = 216

x^2+ 21x = 216-108

x^2 + 21x = 108

x^2 + 21x -108 = 0

let us plug a= 1 b= 21 c= -108 in quadratic formula

x= [-21 + / - ( 21^2 - 4* 1 * -108 )^(1/2 ]/ 2* 1

x= 4.27

Answer :

Both sides are increased by 4.27 feet .