Question

A large suburb currently uses square signs to notify drivers of nearby bike lanes. In order to increase the visibility of these signs, the mayor wants to increase their dimensions. The new sign will be 12 inches longer and 8 inches taller than the current signs. Suppose x represents the side measure of the current signs, in inches. Determine the equation that represents the are,y,in square inches, of the new signs

Answer 1

y = (x +12)(x +8)

or

y = x² +20x +96

Step-by-step explanation:

If the current sign is x inches long, adding 12 inches to the length makes it ...

... length = x + 12

If the current sign is x inches tall, adding 8 inches to the height makes it ...

... height = x + 8

The area of the sign is the product of length and height:

... y = (x +12)(x +8)

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This equation is certainly adequate for finding the area, but some may prefer it in expanded form:

... y = x(x +8) +12(x +8) = x² +8x +12x +96

... y = x² +20x +96