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.

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

Step-by-step 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

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

a; x = 0.5

step-by-step explanation:

-10x = -5

x = 0.5