Chapter 23: Chapter 23

Problem 439

Next question

A rectangle, the lengths of whose base and altitude are in the ratio \(4: 1\), is equivalent to a square, the length of whose side is 6 inches. Find the dimensions of the rectangle.

Short Answer

Expert verified

The dimensions of the rectangle are 12 inches by 3 inches.

See the step by step solution

Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Assign variables to the dimensions of the rectangle

Let the base of the rectangle be 4x, and the altitude be x. We are given that the ratio of the dimensions is 4:1, so this ensures that the ratio is maintained.

Step 2: Write the equation for the area of the rectangle

The area of the given rectangle is the product of its base and altitude: Area of the rectangle = base * altitude = (4x) * (x) = 4x^2

Step 3: Write the equation for the area of the square

The given square has side length of 6 inches. The area of the square is the side length squared: Area of the square = side^2 = 6^2 = 36 square inches.

Step 4: Set the area of the rectangle equal to the area of the square and solve for x

Since the area of the rectangle is equivalent to the area of the square, we can set their areas equal and solve for x: 4x^2 = 36 Now, divide both sides by 4 to solve for x^2: x^2 = 9 Take the square root of both sides to find x: x = 3

Step 5: Find the dimensions of the rectangle

Now that we know the value of x, we can find the dimensions of the rectangle: Base = 4x = 4 * 3 = 12 inches Altitude = x = 3 inches The dimensions of the rectangle are 12 inches by 3 inches.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Recommended explanations on Math Textbooks

Select your language

Chapter 23: Chapter 23

A rectangle, the lengths of whose base and altitude are in the ratio \(4: 1\), is equivalent to a square, the length of whose side is 6 inches. Find the dimensions of the rectangle.

Short Answer

Step by step solution

Unlock all solutions

Step 1: Assign variables to the dimensions of the rectangle

Step 2: Write the equation for the area of the rectangle

Step 3: Write the equation for the area of the square

Step 4: Set the area of the rectangle equal to the area of the square and solve for x

Step 5: Find the dimensions of the rectangle

Access millions of textbook solutions in one place

Most popular questions from this chapter

More chapters from the book ‘Geometry’

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Chapter 20

Chapter 21

Chapter 22

Chapter 24

Chapter 25

Chapter 26

Chapter 27

Chapter 28

Chapter 29

Chapter 30

Chapter 31

Chapter 32

Chapter 33

Chapter 34

Chapter 35

Chapter 36

Chapter 37

Chapter 38

Chapter 39

Chapter 40

Chapter 41

Chapter 42

Chapter 43

Chapter 44

Chapter 48

Chapter 49

Chapter 50

Chapter 51

Chapter 52

Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Calculus

Statistics

Pure Maths

Geometry

Mechanics Maths

Decision Maths