Super-Hard SAT Math Question 68 | Free SAT Prep | Aniko

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Question 68·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

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A city planning map uses the scale 1 inch represents 3 miles. On the map, a rectangular nature preserve measures 6.35 centimeters by 4.57 centimeters.

Which choice is closest to the actual area of the preserve in square kilometers, rounded to the nearest tenth? (Use $1\text{ inch}=2.54\text{ centimeters}$ and $1\text{ mile}=1.609\text{ kilometers}$ .)

For scale problems, convert all measurements into compatible units before applying the scale. Compute the area only after both side lengths are in the same real-world unit. Finally, remember that converting from miles to kilometers affects area by $(1.609)^2$ (not $1.609$ ), since area units are squared.

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Convert units on the map first

The side lengths are in centimeters, but the scale uses inches. Convert cm to inches using $1\text{ in}=2.54\text{ cm}$ .

Apply the map scale to each side

After you have inches, multiply each side length by $3$ to get miles.

Compute area in square miles

Multiply the actual length and width (in miles) to get the area in square miles.

Square the miles-to-kilometers factor

Because $1\text{ mile}=1.609\text{ km}$ is a length conversion, converting area requires multiplying by $(1.609)^2$ .

Desmos Guide

Convert cm to inches

Enter Lin=6.35/2.54 and Win=4.57/2.54.

Convert inches to miles using the scale

Enter Lmi=Lin*3 and Wmi=Win*3.

Compute area and convert to km^2

Enter Ami=Lmi*Wmi and then Akm=Ami*(1.609)^2.

Round and match

Round Akm to the nearest tenth and select the matching answer choice.

Step-by-step Explanation

Convert centimeters to inches

Use $1\text{ inch}=2.54\text{ cm}$ .

$6.35\text{ cm} \div 2.54 = 2.5$ inches
$4.57\text{ cm} \div 2.54 \approx 1.799$ inches

Use the scale to convert inches to miles

Using 1 inch $=3$ miles:

Length: $2.5\cdot 3=7.5$ miles
Width: $1.799\cdot 3\approx 5.398$ miles

Find the area in square miles

The preserve is rectangular, so

A\approx 7.5\times 5.398\approx 40.48

So the area is about $40.48\text{ mi}^2$ .

Convert square miles to square kilometers

Since $1\text{ mile}=1.609\text{ km}$ , areas scale by $(1.609)^2$ :

A\approx 40.48\cdot (1.609)^2

Round to the nearest tenth

Compute $(1.609)^2\approx 2.588881$ , so

A\approx 40.48\cdot 2.588881\approx 104.8

Rounded to the nearest tenth, the area is 104.8 square kilometers.

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation