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The perimeter of a triangle is 65 in. The longest side is 14 in. longer than the medium​ side, and the medium side is 6 in. more than the shortest side. Find the length of each side of the triangle.

User Icon for Bosnian Bosnian answered
3 years ago

l = the longest side

m = the medium side

s = the shortest side

The longest side is 14 in longer than the medium​ side means:

l = m + 14

The medium side is 6 in more than the shortest side means:

m = s + 6

Replace this value in equation:

l = m + 14

l = s + 6 + 14

l = s + 20

The perimeter:

P = s + m + l = 65

s + s + 6 + s + 20 = 65

3 s + 26 = 65

Subtract 26 to both sides

3 s = 39

Divide both sides by 3

s = 13 in

m = s + 6 = 13 + 6 = 19 in

l = s + 20 = 13 + 20 = 33 in

the longest side = 33 in

the medium side = 19 in

the shortest side = 13 in

The perimeter:

P = s + m + l = 13 + 19 + 33 = 65 in

User Icon for Explain Bot Explain Bot answered
11 months ago

To solve this problem, let's start by assigning variables to the lengths of the sides of the triangle. Let's call the shortest side x inches.

According to the problem, the medium side is 6 inches more than the shortest side. So the medium side would be (x + 6) inches.

The longest side is given as 14 inches longer than the medium side. So the longest side would be (x + 6 + 14) inches, which simplifies to (x + 20) inches.

The perimeter of a triangle is the sum of the lengths of all three sides. So we can set up the following equation:

x + (x + 6) + (x + 20) = 65

Now, let's solve for x:

3x + 26 = 65

Subtracting 26 from both sides:

3x = 39

Dividing both sides by 3:

x = 13

So the shortest side is 13 inches.

Plugging this value back into our expressions for the medium and longest sides, we get:

Medium side = x + 6 = 13 + 6 = 19 inches
Longest side = x + 20 = 13 + 20 = 33 inches

Therefore, the lengths of the sides of the triangle are 13 inches, 19 inches, and 33 inches.