Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The areas of two mathematically similar shapes are in the ratio
49:81
The length of the smaller shape is
24.5cm
Work out the length of the larger shape.

The areas of two mathematically similar shapes are in the ratio $49:81$ . The length of the smaller shape is $24.5\,\text{cm}$ . Work out the length of the larger shape.

View step-by-step help

View step-by-step help

Convert between customary and metric systems

Full solution

Q. The areas of two mathematically similar shapes are in the ratio

49:81

. The length of the smaller shape is

24.5\,\text{cm}

. Work out the length of the larger shape.

Understand Relationship: Understand the relationship between the areas of similar shapes and their corresponding lengths. $\newline$ The ratio of the areas of similar shapes is equal to the square of the ratio of their corresponding lengths. This means that if the areas are in the ratio $49:81$ , then the lengths are in the ratio $\sqrt{49}:\sqrt{81}$ , which simplifies to $7:9$ .
Calculate Length of Larger Shape: Calculate the length of the larger shape using the ratio of lengths. $\newline$ We know the length of the smaller shape is $24.5\,\text{cm}$ , which corresponds to the smaller number in the ratio of lengths ( $7$ ). To find the length of the larger shape, we set up a proportion: $\newline$ $\frac{\text{smaller length}}{\text{larger length}} = \frac{\text{smaller ratio number}}{\text{larger ratio number}}$ $\newline$ $\frac{24.5\,\text{cm}}{\text{larger length}} = \frac{7}{9}$
Solve Proportion: Solve the proportion for the length of the larger shape. $\newline$ $(\text{larger length}) = \frac{24.5 \, \text{cm} \times 9}{7}$ $\newline$ $(\text{larger length}) = \frac{220.5 \, \text{cm}}{7}$ $\newline$ $(\text{larger length}) = 31.5 \, \text{cm}$

More problems from Convert between customary and metric systems

Question

\newline

1

2

\_\_\_\_\_

Posted 7 months ago

Question

710

milliliters of energy drink yesterday. How many liters of energy drink did he consume?

\newline

(Round your answer to the nearest hundredth of a liter.)

Posted 8 months ago

Question

A real estate purveyor purchases a

60

000

\left(\mathrm{ft}^{2}\right)

warehouse and decides to turn it into a storage facility. The warehouse's width is exactly

\frac{2}{3}

of its length. What is the warehouse's width? Round your answer to the nearest foot.

Posted 8 months ago

Question

3

cups (c) of flour to bake

2

loaves of bread. If

1

pound (lb) of flour is equivalent to

3 \frac{1}{3} \mathrm{c}

, how many loaves of bread can the baker make with a

10 \mathrm{lb}

\newline

(Round the answer to the nearest whole number.)

Posted 7 months ago

Question

\$ 2500

into a savings account.

\newline

The relationship between the time,

t

, in years, since the account was first opened, and Ella's account balance,

B(t)

, in dollars, is modeled by the following function.

\newline

B(t)=2500 \cdot e^{0.025 t}

\newline

What will the balance of Ella's savings account be after

4

years? Round your answer, if necessary, to the nearest hundredth.

\newline

\$

Posted 8 months ago

Question

Maya needs to rent a car while on vacation. The rental company charges

\$17.95

18

cents for each mile driven. If Maya only has

\$40

to spend on the car rental, what is the maximum number of miles she can drive?

\newline

\newline

(Round your answer down to the nearest whole mile)

Posted 8 months ago

Question

What is the area of a circle whose circumference is

1447

\pi=3.14

166698.73\,\text{m}^2

Posted 8 months ago

Question

What is the area of a circle whose circumference is

1447

\pi = 3.14

166698.73 \, \text{m}^2

Posted 7 months ago

Question

13

feet to meters using

3.281

1

\newline

Round answers to hundredths of meters (or

2

decimal places)

Posted 8 months ago

Question

14

feet to meters using

3.281

1

\newline

Round answers to hundredths of meters (or

2

decimal places)

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant