SOLUTION: 1. Tom�s uncle owns a triangular piece of land. The perimeter fence that surrounds the land measures 378 yards. The shortest side is 30 yards longer than one-half of the longest si

Question 142453: 1. Tom�s uncle owns a triangular piece of land. The perimeter fence that surrounds the land measures 378 yards. The shortest side is 30 yards longer than one-half of the longest side. The second longest side is 2 yards shorter than the longest side. What is the length of each side?
2. In an auditorium there are 4x rows, and each row can accommodate 5yz benches. If x students can be accommodated in each bench, then how many students can sit in the auditorium?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. Tom�s uncle owns a triangular piece of land. The perimeter fence that surrounds the land measures 378 yards. The shortest side is 30 yards longer than one-half of the longest side. The second longest side is 2 yards shorter than the longest side. What is the length of each side?
:
Let x = longest side length
;
Write an expression for each statement:
:
"The shortest side is 30 yards longer than one-half of the longest side.:
(.5x + 30) = shortest side
:
"The second longest side is 2 yards shorter than the longest side."
(x-2) = 2nd longest side
:
The perimeter equation (the 3 sides = 378)
x + (.5x + 30) + (x-2) = 378
:
x + .5x + x + 30 - 2 = 378; combine like terms
:
2.5x + 28 = 378
:
2.5x = 378 - 28; subtracted 28 from both sides
;
2.5x = 350
x = ; divided both sides by 2.5
x = 140 yds is the longest side
then
.5(140) + 30 = 100 yds the shortest side
and
140 - 2 = 138 yds the 2nd longest side
;
Check solution by finding the perimeter using these values
140 + 100 + 38 = 378
:
:
2. In an auditorium there are 4x rows, and each row can accommodate 5yz benches. If x students can be accommodated in each bench, then how many students can sit in the auditorium?
:
The total benches:
4x * 5yz = 20xyz benches
:
The total students
x * 20xyz = students
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