math
posted by Toni .
the perimeter of a triangle is 54 centimeters. the longest side is 6 centimeters less than the sum of the other two sides. Twice the shortest side is 10 centimeters less than the longest side. Find the lengths of each side of the tirangle

shortest side  x
longest  2x + 10
let middle side be y
2x + 10 = x + y 6
y = x+16
so x + 2x+10 + x+16 = 54
4x = 28
x = 7
shortest side = 7
longest side = 24
middle side = 23
check: is the sum = 54 ? yes!
is 24 equal to 6 less than 30 ?, yes
is twice 7 10 less than 24 ? yes!
All is good!
Respond to this Question
Similar Questions

ALGEBRA II
the perimeter of a triangle is 51 centimeters, the longest side is 1 centimeter less than the sum of the other two sides. twice the shortest is 11 centimeters less than the longest side. find the lengths of each side of the triangle. 
Algebra
The backyard of a house is in the shape of a triangle. The longest side is 4 ft shorter than twice the shortest side. The third side is 4 ft less than the longest side. If the perimeter of the yard is 162 ft, what are the lengths of … 
Intermediate Algebra
The perimeter of a triangle is 48 centimeters. The longest side is 2 centimeters less than the longest side. Find the lengths of each side of the triangle. 
Algebra
The perimeter of a triangle is 52 centimeters. The longest is 2 centimeters less than the sum of the other 2 sides. Twice the shortest side is 13 centimeters less than the longest side. Find the lengths of each side of the triangle. … 
ALGEBRA
The perimeter of a triangle is 52 centimeters. The longest is 2 centimeters less than the sum of the other 2 sides. Twice the shortest side is 13 centimeters less than the longest side. Find the lengths of each side of the triangle. … 
Math
The perimeter of a triangle is 19 cm. If the length of the longest side is twice that of the shortest side and 3 cm less than the sum of the lengths of the other two sides, find the lengths of the three sides 
Algebra
the perimeter of a triangle is 56 inches. the longest side measures 4 inches less than the sum of the other two sides. three times the shortest side is 4 inches more than the longest side. find the lengths of the three sides 
algebra
The perimeter of a triangle is 45 centimeters. Find the lengths of its sides, if the longest side is 7 centimeters longer than the shortest side, and the remaining side is 2 centimeters longer than the shortest side. 
Algebra 2
the perimeter of a triangle is 19 cm. if the length of the longest side is twice that of the shortest side and 3cm less than the sum of the lengths of the other two sides, find the length of the three sides 
Algebra
The perimeter of a triangle is 60 cm. The longest side exceeds the shortest one by 10 cm.and the sum of the lengths of the longest and the shortest ones is twice the length of the other side. Find the lengths of the sides.