# Conor wants to put a moat around his rectangular castle. Let m= the width of the moat. The castle is 60 ft X 45 ftWrite a polynomial that represent the total area of the castle and moat. Find the...

Conor wants to put a moat around his rectangular castle. Let m= the width of the moat. The castle is 60 ft X 45 ft

Write a polynomial that represent the total area of the castle and moat. Find the combined area if the moat is 10 feet wide. If the moat is also 10 feet deep, calculate how many gallons of water are in the moat if 1 gallon=0.134 ft^3.

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### 2 Answers

The rectangular castle has dimensions 60 ft X 45 ft. The total area of the castle is A = 60*45 = 2700 ft^2.

If the width of the moat is m, the total area of the moat is 120*m + 90*m + 4*m^2.

Given the width of the moat is 10 ft, the combined area of the moat is 120*10 + 90*10 + 4*100 = 2500 ft^2.

The depth of the moat is 10 ft which gives a volume of 25000 ft^3 = 25000/0.134 = 185,185 gallons.

**The moat has 185,185 gallons of water.**

Dimensions of castle = 60ftx45ft

Area of Castle = 60*45 = 2700 sqft

Width of moat = 10ft

outer dimensions of moat = (60+2*10)ftx(45+2*10)ft = 80ftx65ft

**Combined area of Castle and moat = 80*65 = 5200 sqft**

Area of moat = 5200 - 2700 = 2500 sqft

Depth of moat = 10ft

Volume of moat = 2500*10 = 25000 ft^3 = 25000/0.134 = 185,185 gallons

**Volume of water in moat = 185,185 gallons**