SOLUTION: I need your help please, A triangle has a perimeter of 161 miles. Each of the two smaller sides are two thirds the length of the longest side. Find the length of each side of the t

Algebra ->  Triangles -> SOLUTION: I need your help please, A triangle has a perimeter of 161 miles. Each of the two smaller sides are two thirds the length of the longest side. Find the length of each side of the t      Log On


   

Question 73296This question is from textbook college algebra
: I need your help please, A triangle has a perimeter of 161 miles. Each of the two smaller sides are two thirds the length of the longest side. Find the length of each side of the triangle. This question is from textbook college algebra

Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) About Me  (Show Source):
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: a+=+%282%2F3%29b. Now you want to substitute this relationship into the equation for the perimeter.
161+=+2%282%2F3%29b%2Bb Simplify and solve for b.
161+=+%284%2F3%29b%2Bb
161+=+%287%2F3%29b Multiply both sides by the multiplicative inverse of 7%2F3, that's 3%2F7.
161%283%2F7%29+=+b Simplify.
23%2A3+=+b
b+=+69mil;es. This is the length of the longest side.
a+=+%282%2F3%29b
a+=+%282%2F3%2969
a+=+46miles. This is the length of each of the short sides.
Check:
46+46+69 = 161

Answer by jim_thompson5910(35256) About Me  (Show Source):
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
y=%282%2F3%29x
Since the perimeter is the sum of all the sides then
P=x%2By%2By
161=x%2B%282%2F3%29x%2B%282%2F3%29xPlug in 2/3x into y
161=x%2B%284%2F3%29xAdd like terms by finding common denominator
161=%283x%2B4x%29%2F3Solve for x
483=%287x%29Multiply both sides by 3
69=xDivide both sides by 7
So the longest side is 69 miles. Take two thirds of it to find the shorter side.
y=%282%2F3%29%2869%29
y=46
So the shorter sides are 46 miles
Check:
Use the formula to find the perimeter
P=x%2By%2By
161=69%2B46%2B46
161=161Answer works