Question

The perimeter of a triangle is 16√7 feet. If two of the sides measure √343 feet and √175, find the length of the third side as a radical in simplest form.

Answer 1

• 5√7 feet

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Given:

• The perimeter of a triangle - 16√7 feet,
• Two of the sides - √343 feet and √175 feet.

First, convert the two side length as below:

• √343 = √(49*7) = 7√7,
• √175 = √(25*7) = 5√7.

Now find the third side:

• 17√7 - (7√7 + 5√7) =
• 17√7 - 12√7 =
• 5√7

Hence the third side is 5√7 feet.