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In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle?

 Jan 6, 2021

Best Answer 

 #1
avatar+292 
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If the second side has length x,

Then the first side has length 3x,

We know that the third side which has length 17.

Now, by the triangle inequality, we have:

x + 17 > 3x

=> 2x < 17

=> x < 8.5

Since we want the greatest perimeter,so we need the greatest integer x, and if x < 8.5.

Then x = 8

Then, the first side has length -> 3 x 8 = 24

The second side has length = 8 cm

The third side has length = 17 cm

So,perimeter = 17 + 24 + 8 = 49 cm

 Jan 6, 2021
 #1
avatar+292 
+1
Best Answer

If the second side has length x,

Then the first side has length 3x,

We know that the third side which has length 17.

Now, by the triangle inequality, we have:

x + 17 > 3x

=> 2x < 17

=> x < 8.5

Since we want the greatest perimeter,so we need the greatest integer x, and if x < 8.5.

Then x = 8

Then, the first side has length -> 3 x 8 = 24

The second side has length = 8 cm

The third side has length = 17 cm

So,perimeter = 17 + 24 + 8 = 49 cm

hihihi Jan 6, 2021

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