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Question

devins rectangular garden is 6 yards long and 4 yards wide. he plans to double the area of the garden by increasing each side by the same amount. find the number of meters by which each dimension must be increased.

Answer 1

The current area of the garden is 6 x 4 = 24 yd². Doubling the area would result in an area of 48 yd². If he is going to increase each side by the same amount, let's call that amount x. We have the following equation:

 

(6 + x)(4 + x) = 48

24 + 10x + x² = 48

x² + 10x - 24 = 0

(x - 2)(x + 12) = 0

The only logical solution is x = 2 since dimensions cannot be negative. Therefore, each dimension must be increased by 2 yd. If we do, we see that the new dimensions of the garden will be 8 x 6 = 48 yd², which is double the original area of the garden.