quadratic word problem

Question

1. The length of a rectangle is 3 feet greater than four times its width. Find the length and width of the rectangle if its area is 76 square feet.

Answer 1

We know two formulas

L*W =76

L=4w+3

So we solve for L in both formulas

L=76/w

Therefore 76/w = 4w+3

76= 4w^2 +3w

4w^2 +3w - 76 =0

(w-4)(4w+19)=0

W=4

Plug W back into l*w=76

4l=76

L= 19

Answer 2

To answer your question,

I would start by drawing a rectangle on a piece of paper. You know that the length is "3 feet greater than four times its width", but you still do not know what the width is. You can start by labeling the width "x". Then you can create an expression that represents the length based on x (the width). The formula for the area of a rectangle is A (area)=l (length) w (width).

You can then substitute in x for the width and the expression you came up with for the length. The A (area) is given as 75 square feet.

You then have an equation with a single variable that you can use to solve for x.

This new equation should be a quadratic function: ax^2 +bx+c

You can then use the quadratic formula in order to determine the values of x

If you calculate a negative value using the quadratic formula that cannot be the value of x because you cannot have a negative width. Instead, the positive value of x must be the width.

Then substitute your calculated x value into the expression you created earlier to represent the length. The solution to that is the length!

I hope this helps!