Arectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 determine the solutions of the equation. what solution makes sense for the situation? x = what are the dimensions of the rectangle? width = inches length = inches

Step-by-step explanation:

x² + 5x – 104 = 0

Factor using the AC method.  Here, a = 1 and c = -104.  Multiplied together, ac = -104.  Factors of -104 that add up to +5 are +13 and -8.

(x + 13) (x - 8) = 0

x = -13, 8

A negative width doesn't make sense, so x = 8.  Therefore, the width is 8 inches and the length is 5 more than that, or 13 inches.

width = 8

length = 13

Step-by-step explanation:

All that is left to do is factor the results that you have

x^2 + 5x - 104 = 0

You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.

The two numbers are 8 and 13

More formally stated, the quadratic can be factored to

(x + 13)(x - 8) = 0

x - 8 =0

x - 8 + 8 = 8 + 0

x = 8

x + 13 = 0 has no meaning.

That means that the width ( a positive number ) = 8

The length is 5 more = 13

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