/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 83 A rectangular parking lot has a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 83

A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 180 square yards. Find the length and the width.

Short Answer

Expert verified
The width of the parking lot is 15 yards, and the length is 18 yards.

Step by step solution

01

Define the variables

Let's define \(x\) as the width of the parking lot. According to the problem, the length of the parking lot is 3 yards greater than the width. So, the length is \(x + 3\) yards.
02

Write the equation

The area of the parking lot is given as 180 square yards. Since the area of a rectangle is length x width, we can set up the equation: \(x(x + 3) = 180\).
03

Solve the equation

Rewrite the equation to the standard quadratic form \(ax^2 + bx + c = 0\): \[x^2 + 3x - 180 = 0\]. Factor the equation, \[(x - 15)(x + 12) = 0\] The possible solutions are \(x = 15\) and \(x = -12\). Since width cannot be negative, we only accept the positive solution, \(x = 15\).
04

Find the Length

Now, substitute \(x = 15\) into the equation for the length (\(x + 3\)) yielding \(15 + 3 = 18\). So, the length of the parking lot is 18 yards.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The formula $$S=2 x^{2}-12 x+82$$ models spending by international travelers to the United States, \(S,\) in billions of dollars, \(x\) years after \(2000 .\) Use this formula to solve. In which years did international travelers spend \(\$ 72\) billion?

In Exercises \(130-133,\) use the \([\mathrm{GRAPH}]\) or \([\mathrm{TABLE}]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If the graphs of \(y_{1}\) and \(y_{2}\) coincide, or if their corresponding table values are equal, this means that the polynomial on the left side has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$x^{3}-1=(x-1)\left(x^{2}-x+1\right)$$

Exercises \(137-139\) will help you prepare for the material covered in the next section. In each exercise, factor completely. $$x^{3}-2 x^{2}-x+2$$

In Exercises \(130-133,\) use the \([\mathrm{GRAPH}]\) or \([\mathrm{TABLE}]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If the graphs of \(y_{1}\) and \(y_{2}\) coincide, or if their corresponding table values are equal, this means that the polynomial on the left side has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$x^{2}-6 x+9=(x-3)^{2}$$

The second angle of a triangle measures three times that of the first angle's measure. The third angle measures \(80^{\circ}\) more than the first. Find the measure of each angle. (Section \(2.6,\) Example 6 )
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.