You can
put this solution on YOUR website!From the problem description, we can see that the triangle is an isosceles triangle. So we let the two equal sides be of length a and the third side, length b.
As you no doubt already know, the perimeter of a triangle is equal to the sum of the three sides, so P = a+a+b = 2a+b
But you are told that p = 161 miles, so now you can write the equation required to solve the problem:
161 = 2a+b
You also know that each of the two equal sides (a) is equal to two-thirds of the third side (b). This can be written:
. Now you want to substitute this relationship into the equation for the perimeter.
Simplify and solve for b.
Multiply both sides by the multiplicative inverse of
, that's
.
Simplify.
mil;es. This is the length of the longest side.
miles. This is the length of each of the short sides.
Check:
46+46+69 = 161
You can
put this solution on YOUR website!Let x be the longest side and y be the shorter sides. If you have the two smaller sides equal to two thirds of the longest side it looks like this
Since the perimeter is the sum of all the sides then
Plug in 2/3x into y
Add like terms by finding common denominator
Solve for x
Multiply both sides by 3
Divide both sides by 7
So the longest side is 69 miles. Take two thirds of it to find the shorter side.
So the shorter sides are 46 miles
Check:
Use the formula to find the perimeter
Answer works
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