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Q30.

Expert-verified

Geometry

Found in: Page 427

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

A wooden fence high and 220ft long is to be painted on both sides.
What is the total area to be painted?
A gallon of a certain type paint will cover only $200 f t^{2}$ of area for the first coat, but on the second coat a gallon of the same paint will cover $300 f t^{2} .$ If the fence is to be given two coats of paint, how many gallons of paint should be bought?

The area to be painted is $2640 f t^{2}$
Total paint required is22 gallon.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Length of the wooden fence $= 6 f t$

Height of the wooden ffence $= 220 f t$

Step 2. Concept Used.

If bis the length of the wooden fence and h is the height of the fence.

Then, the area of the fence is $A = b \times h$

Step 3. Let’s calculate the area of the fence.

Put the value of length and height into the formula and find the area.

Area of the fence : $\begin{matrix} A = 220 \times 6 \\ = 1320 f t^{2} \end{matrix}$

Since, it is to be painted on both sides the painted area gets doubled

i.e.

$\begin{array}{l} A = 2 \times 1320 \\ A = 2640 f t^{2} \end{array}$

So, area to be painted is $2640 f t^{2}$

In the first coat $200 f t^{2} = 1$

gallon

Then, $2640 f t^{2} = (\frac{2640}{200}) = 13.2$

gallon

In the second coat $300 f t^{2} = 1$

gallon

Then, $2640 f t^{2} = (\frac{2640}{300}) = 8.8$

gallon

Thus $= (13.2 + 8.8) = 22$

Total paint gallon

Therefore, the area to be painted is $2640 f t^{2}$ and total paint required is 22gallon.

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