Question

1. Homer has an idea for a new donut shop. He wants to design the donut shop so that the rectangular

Answer 1

Solving a system of equations, it is found that since the quadratic equation has two positive roots, they can be the values of the length and the width, and the design is possible.

The perimeter of a rectangle of length l and width w is given by:

$P = 2(l + w)$

The area is:

$A = lw$

In this problem, perimeter of 63.5 m, hence:

$2l + 2w = 63.5$

$2l = 63.5 - 2w$

$l = 31.75 - w$

Area of 225 m², hence:

$lw = 225$

$(31.75 - w)(w) = 225$

$w^2 - 31.75w + 225 = 0$

Which is a quadratic equation with coefficients $a = 1, b = -31.75, c = 225$.

Then:

$\Delta = b^2 - 4ac = (-31.75)^2 - 4(1)(225) = 108.0625$

$w_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{31.75 + \sqrt{108.0625}}{2} = 21.1$

$w_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{31.75 - \sqrt{108.0625}}{2} = 10.68$

Since the quadratic equation has two positive roots, they can be the values of the length and the width, and the design is possible.

A similar problem is given at brainly.com/question/10489198