SOLUTION: The perimeter of an equilateral triangle is 45 inches.A rectangle whose width is 1-3 its length has a perimeter of 48 inches.Which figure has the longest side and why?

Question 282202: The perimeter of an equilateral triangle is 45 inches.A rectangle whose width is 1-3 its length has a perimeter of 48 inches.Which figure has the longest side and why?
Found 2 solutions by dabanfield, oberobic:
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
The perimeter of an equilateral triangle is 45 inches.A rectangle whose width is 1-3 its length has a perimeter of 48 inches.Which figure has the longest side and why?
The equalateral triangle has equal sides so each side has length 45/3 = 15.
If w is the width of the rectangle and 3w is the length then the perimeter is:
2*w + 2*(3w) = 48
8*w = 48
w = 6
The length is 3*w = 3*6 = 18 so the rectangle's length is the longest side of the two figures.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The perimeter of an equilateral triangle = 3s, where s=length of the each side.
3s = 45
s = 15
.
A rectangle has perimeter = 2(l+w)
We're told
w = l-3 and perimeter = 48
48 = 2(l + l-3)
2(2l -3) = 48
2l -3 = 24
2l = 27
l = 13.5
.
w = l-3 = 13.5-3 = 10.5
.
checking perimeter
2(13.5 + 10.5) = 48??
2(24) = 48
correct!
so
l = 13.5
w = 10.5
.
The question asks which figure has the longest side.
Answer:
Equilateral triangle has the longest sides at 15 inches.
.
Done
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