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Question

An exercise yard is enclosed with 476 1/24 feet of security fencing. Three sides are 102 2/3 feet, 125 3/4 feet, and 120 5/8 feet. What’s the length of the fourth side?

Answer 1

Think of this problem as consisting of parts making up a whole. All the sides bust add up to the entire security fencing. We know three sides and the total length of all sides. We can subtract each of the three sides from the total length to get the last side!

To put this in terms of math:

476 1/24 = 102 2/3 + 125 3/4 + 120 5/8 + x,

where x is the fourth side.

Let's add the first two sides together first.

102 2/3 + 125 3/4 = 227 + 2/3 + 3/4

Using a least common denominator of 12:

227 + 8/12 + 9/12 = 227 + 17/12 = 227 + 1 + 5/12 = 228 5/12

Now lets add this sum to the third side.

228 5/12 + 120 5/8 = 348 + 5/12 + 5/8

Using a least common denominator of 24:

348 + 10/24 + 15/24 = 348 + 25/24 = 348 + 1 1/24 = 349 1/24

With this sum, we can simplify

476 1/24 = 102 2/3 + 125 3/4 + 120 5/8 + x

to

476 1/24 = 349 1/24 + x

Solving for x:

x = 476 1/24 - 349 1/24

= 127 ft.

Therefore, the length of the fourth side is 127 ft.

Answer 2

To find the length of the fourth side of the exercise yard, we need to subtract the combined lengths of the three known sides from the total length of the fencing.

Given:

1. Total length of the fencing: 476124476241​ feet
2. Length of the three known sides: 102 2/3 feet, 125 3/4 feet, and 120 5/8 feet

First, let's convert all lengths to the same format (fractions or mixed numbers). Since the total length of the fencing is given as a mixed number, let's convert the lengths of the known sides to mixed numbers:

102 2/3 feet = 30833308​ feet

125 3/4 feet = 50344503​ feet

120 5/8 feet = 96988969​ feet

Now, let's find the combined length of the three known sides:

Combined length of three sides=3083+5034+9698

Combined length of three sides=3308​+4503​+8969​

To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 3, 4, and 8, which is 24.

Then, we'll convert each fraction to have a denominator of

24:3083

308×83×8=2464243308​=3×8308×8​=242464​ 5034=503×64×6=3018244503​=4×6503×6​=243018​ 9698=969×38×3=2907248969​=8×3969×3​=242907​

Now, let's add them:

Combined length of three sides=246424+301824+290724Combined length of three sides=242464​+243018​+242907​ =2464+3018+290724=242464+3018+2907​ =838924=248389​

Now, let's subtract this combined length from the total length of the fencing:

Length of fourth side=476124−838924Length of fourth side=476241​−248389​

To subtract these mixed numbers, we need to convert 476 to have a denominator of 24:

476124=476×24+124=1142524476241​=24476×24+1​=2411425​

Now, let's subtract:

Length of fourth side=1142524−838924Length of fourth side=2411425​−248389​ =11425−838924=2411425−8389​ =303624=243036​ =1271=1127​

Therefore, the length of the fourth side of the exercise yard is 127124127241​ feet.