Question

Johnny B's rectangular garden is 5 feet long and 10 feet wide. He wants to make the area of his garden 6 times as large by increasing the length and width by the same amount. Find the number of feet by which each dimension must be increased.

Answer 1

Each dimension must be increased by 10 feet in order to make the area 6 times larger.

Explanation:

To solve this problem we first need to calculate the area of his garden before the change, this can be done by using the formula below:

area = length*width

area = 5*10 = 50 feet²

He wants the new area to be 6 times as large, therefore it should be 6*50 = 300 feet². Assuming the length and width will be increased by "x", we have:

new area = (length+x)(width + x)

300 = (5 + x)(10 + x)

300 = 50 + 5x + 10x + x²

x² + 15x + 50 - 300 = 0

x² + 15x - 250 = 0

delta = sqrt(b² - 4ac) = sqrt(15² - 4*1*(-250)) = sqrt(225 +1000) = sqrt(1225) = 35

`x = (-15 \pm35)/2*1\\x_1 = (-15 - 35)/2 =-25\\x_2 = (-15 + 35)/2 = 10`

Since we want to increase the area the only possible solution must be x = 10.