Question

this question has two parts. first, answer part a. then, answer part b. part a a map of a rectangular park has a length of 4 inches and a width of 6 inches. it uses a scale of 1 inch for every 30 miles. what is the actual area of the park? square miles part b the map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. at what scale should the map be reproduced so that it fits on the brochure? 1 inch = miles (lesson 1 - 12)

Explanation:

Step1: Find actual length

Since 1 inch represents 30 miles and map - length is 4 inches, actual length $l = 4\times30=120$ miles.

Step2: Find actual width

Since 1 inch represents 30 miles and map - width is 6 inches, actual width $w = 6\times30 = 180$ miles.

Step3: Calculate actual area

Area of rectangle $A=l\times w$, so $A = 120\times180=21600$ square miles.

Step4: Find original map area

Original map area $A_{map1}=4\times6 = 24$ square inches.

Step5: Let new scale be 1 inch = $x$ miles

Let the new length on map be $a$ inches and new width be $b$ inches, and $A_{map2}=ab = 6$ square inches.
Let the actual length and width remain the same. So actual length $l = 120$ miles and actual width $w = 180$ miles. Then $a=\frac{120}{x}$ and $b=\frac{180}{x}$.
Since $ab = 6$, we have $\frac{120}{x}\times\frac{180}{x}=6$.
Cross - multiply: $120\times180 = 6x^{2}$.
$x^{2}=\frac{120\times180}{6}=3600$.
Take square root of both sides: $x = 60$ miles.

Answer:

Part A: 21600
Part B: 60