# The length of a swimming pool is 8m longer than its width and the area is 105m square. justify the answer by representing each situation by a mathematical sentence.

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We let the width be x, this would make the length x+8 so:

Area = length * width

105 = (x+8)x

105 = x²+8x

0 = x²+8x-105

We look for two numbers with a product of 105 and an absolute difference of 8.

105 - 1 = 104 X

35 - 3 = 32 X

21 - 5 = 16 X

15 - 7 = 8 √

Therefore:

0 = (x+15)(x-7)

So the possible value of x are -15 and 7. We cannot have a negative value since a length is never negative.

So the width is 7m and the length is 15m.

Area = length * width

105 = (x+8)x

105 = x²+8x

0 = x²+8x-105

We look for two numbers with a product of 105 and an absolute difference of 8.

105 - 1 = 104 X

35 - 3 = 32 X

21 - 5 = 16 X

15 - 7 = 8 √

Therefore:

0 = (x+15)(x-7)

So the possible value of x are -15 and 7. We cannot have a negative value since a length is never negative.

So the width is 7m and the length is 15m.