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olchik [2.2K]
3 years ago
10

the smaller rectangle is a 1/4 scale drawing of the original figure. Use the drop-down menus to show the missing dimensions of t

he scale figure.

Mathematics
1 answer:
Neporo4naja [7]3 years ago
4 0

Answer:

Part a) The length of the smaller rectangle is 6\ ft

Part b) The width of the smaller rectangle is 5\ ft

Part c) The area of the smaller rectangle is 30\ ft^{2}

Step-by-step explanation:

Part a)

<u>Find the length side of the smaller figure</u>

we know that

The scale factor is equal to \frac{1}{4}

Remember that

The scale factor is equal to divide the measure of the smaller figure by the corresponding measure of the original figure

so

Let

x--------> the length of the smaller rectangle

y-------> the length of the original figure

z-----> scale factor

z=\frac{x}{y}

we have

y=24\ ft

z=1/4

substitute and solve for x

(1/4)=\frac{x}{24}

x=24/4=6\ ft

Part b)

<u>Find the width side of the smaller figure</u>

we know that

The scale factor is equal to \frac{1}{4}

Remember that

The scale factor is equal to divide the measure of the smaller figure by the corresponding measure of the original figure

so

Let

x--------> the width of the smaller rectangle

y-------> the width of the original figure

z-----> scale factor

z=\frac{x}{y}

we have

y=20\ ft

z=1/4

substitute and solve for x

(1/4)=\frac{x}{20}

x=20/4=5\ ft

Part c)

<u>Find the area of the smaller figure</u>

we know that

The scale factor is equal to \frac{1}{4}

Remember that

The scale factor squared is equal to divide the area of the smaller figure by the area of the original figure

so

Let

x--------> the area of the smaller rectangle

y-------> the area of the original figure

z-----> scale factor

so

z^{2}=\frac{x}{y}

we have

y=480\ ft^{2}

z=1/4

substitute and solve for x

(1/4)^{2}=\frac{x}{480}

x=480/16=30\ ft^{2}

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