Question

bailey writes the expression g2 14g 40 to represent the area of a planned school garden in square feet. if g = 5, what are the dimensions of the school garden? 20 feet by 2 feet 10 feet by 4 feet 12 feet by 7 feet 15 feet by 9 feet

Answer 1

To solve this, we must first factor g^2 + 14g + 40 to find the side lengths that are being multiplied. The factorization is (g + 4)(g + 10). Now that we have the factors, plug in 5 for g in each factor. So, the dimensions are 15 feet by 9 feet.

Answer 2

15 Feet by 9 Feet

What is quadratic equation?

Quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0,

Where a and b are the coefficients, x is the variable, and c is the constant term.

According to the question the correct quadratic equation is :

$A =g^{2} +14g +40$

By using the formula to find the roots of a quadratic equation.

$D = b^{2} - 4ac$

$D = 14^{2} - 4.1.40\\D = 196 - 160\\D = 36\\D = \sqrt{36} \\D = 6$

Here ,

$q_{1,2} = \frac{-14 + 6}{2} , \frac{-14 - 6}{2}$

= -4 , -10

So , we have two values of the equation

(g+4) , (g+10)

Put g = 5

The value will be ,

g+4 = 9feet , g+10 = 15 feet.

The dimensions of the school garden are 9 feet and 15 feet.

Learn more about roots of a quadratic equation here:

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