Let the length of the interstate be x. Then, one side of the town is 1/2 x and the other side is 2/3 x.
We know that the perimeter of the town is 104 km, so we can write an equation:
x + 1/2 x + 2/3 x = 104
To solve for x, we can simplify the equation:
6/6 x + 3/6 x + 4/6 x = 104
13/6 x = 104
x = 48
Now we know that the length of the interstate is 48 km.
To find the length of the other sides of the town, we can use the ratios given to us:
One side is 1/2 x, so it is 1/2 (48) = 24 km.
The other side is 2/3 x, so it is 2/3 (48) = 32 km.
To find the total length of the two new roads, we simply add the lengths of the two sides:
24 km + 32 km = 56 km
Therefore, Mathville needs 56 km of new road to complete their task.
The town of Mathville is triangular in shape and has a perimeter of 104 km. The interstate borders the southern part of the town, but town residents want to build two more roads, one on each side of the town. The length of one side of the town is ½ the length of the interstate. The length of the other side is 2/3 the length of the interstate. Determine the length of road necessary to complete the town’s task. That is, determine the length of each of the two sides of the town not bordered by the interstate.
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