Question

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

Answer 1

The length of the third side of the triangle is 4√7 feet, obtained by simplifying the radicals of the given sides and using the perimeter of the triangle to solve for the missing length.

Step-by-step explanation:

To find the length of the third side of a triangle with a perimeter of ∖16√7 feet when two sides measure √343 feet and √175 feet, we first simplify the radicals of the given side lengths and then use the perimeter to solve for the third side.

The square root of 343 is equal to √(7²7²7) = 7√7, and the square root of 175 is equal to √(7²5²5) = 5√7. Now we know the perimeter (P) of the triangle must equal the sum of its sides, so:

P = 16√7 = √343 + √175 + third side

16√7 = 7√7 + 5√7 + third side

Combine the like terms:

16√7 = (7+5)√7 + third side

16√7 = 12√7 + third side

Subtract 12√7 from both sides to isolate the third side:

Third side = 16√7 - 12√7

Third side = (16 - 12)√7

Third side = 4√7 feet

Therefore, the length of the third side is 4√7 feet in simplest radical form.

Answer 2

Answer:the length of the third side is 4√7

Step-by-step explanation:

The perimeter of a triangle is 16 to the square root of 7 feet. This is expressed as

Perimeter = 16√7 feet

The perimeter of a triangle is the sum of the length of the three sides of the triangle.

If the two sides measure the square root of 343 feet and the square root of 175, which are expressed as √343 and √175, the third length would be

16√7 - (√343 + √175)

Expressing √343 as a radical, it becomes 7√7

Expressing √175 as a radical, it becomes 5√7

7√7 + 5√7 = 12√7

Therefore, the third length would be

16√7 - 12√7 = 4√7 feet