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Expert-verified Found in: Page 427 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # 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 $200f{t}^{2}$ of area for the first coat, but on the second coat a gallon of the same paint will cover $300f{t}^{2}.$ If the fence is to be given two coats of paint, how many gallons of paint should be bought?

1. The area to be painted is $2640f{t}^{2}$
2. Total paint required is22 gallon.
See the step by step solution

## Step 1. Given information.

Length of the wooden fence$=6ft$

Height of the wooden ffence $=220ft$

## 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 $A=b×h$

## 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 :$\begin{array}{c}A=220×6\\ =1320f{t}^{2}\end{array}$

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

i.e.

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

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

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

gallon

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

gallon

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

gallon

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

gallon

Thus$=\left(13.2+8.8\right)=22$

Total paint gallon

Therefore, the area to be painted is$2640f{t}^{2}$ and total paint required is 22gallon. ### Want to see more solutions like these? 