Answer:
13 cm, 25 cm and 34 cm
Explanation:
Define the variables:
- Let a = shortest side of the triangle.
- Let c = longest side of the triangle.
- Let b = other side of the triangle.
Given the perimeter of the triangle is 72 cm:
⇒ a + b + c = 72
Given the longest side is 4 cm less than the sum of the other two sides:
⇒ c = a + b - 4
Given twice the shortest side is 8 cm less than the longest side.
⇒ c = 2a + 8
Substitute the third equation into the second equation and solve for b:
⇒ c = a + b - 4
⇒ 2a + 8 = a + b - 4
⇒ a + 8 = b - 4
⇒ b = a + 12
Substitute the found expression for b and the third equation into the first equation and solve for a:
⇒ a + b + c = 72
⇒ a + (a + 12) + (2a + 8) = 72
⇒ 4a +20 = 72
⇒ 4a = 52
⇒ a = 13
Substitute the found value of a into the other expressions to find b and c:
⇒ b = a + 12
⇒ b = 13 + 12
⇒ b = 25
⇒ c = 2a + 8
⇒ c = 2(13) + 8
⇒ c = 26 + 8
⇒ c = 34
Therefore the lengths of the sides of the triangle are: