Question

Julius has a garden that has dimensions of 12 ft by 20 ft. Julius needs more room to plant some peppers, and determines the garden will need a new area of 360 square feet. How much should he increase the length and width by, if he wants to increase them by the same amount?

Answer 1

The garden that has dimensions of 12 ft by 20 ft has an area:A = 12 x 20 = 240ft².Julius needs a new area: 360ft²;( 12 + x ) · ( 20 + x ) = 360240 + 12 x + 20 x + x² = 360x² + 32 x + 240 - 320 = 0x² + 32 x - 120 = 0x 1/2 = ( - 32 +/- √( 1024 + 480 ) )/ 2x = ( -32 + 38.78 ) / 2 ( another solution is negative )x = 3.39 ≈ 3.4 ftWe can prove it: A ( new ) = ( 12 + 3.4 ) · ( 20 + 3.4 ) = = 15.4 · 23.4 = 360.34 ≈ 360 ft²Answer: He should increase the length and width by the amount of 3.4 ft.