Solving Word Problems with the quadratic formula

Question

A rectangle has sides of length x feet and 2x+2 feet with an area of 24 square feet. Cassandra uses the quadratic formula and finds that x equals 3 and -4. She determines that this means the sides of the rectangle are -4 by -6 or 3 by 8. Why is she incorrect?

Answer 1

When we set up and solve the quadratic equation for this problem we discard the negative

values in the final answer because length and width of the sides of a rectangle are always

considered to be a positive number.  If the problem is worked to the correct solution then

the final answer is the rectangle is 3 by 8.

 

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We can check that easily enough. 

x = 3

2x+2 = 8

 

and (3ft)(8ft) = 24 ft²

 

The only reason she is incorrect is because she said the rectangle could also be -4 by -6

Which by the way does also satisfy the equation.