Does the triangle with the side lengths of 6ft, 7ft, and 8 ft form a right triangle

  No.

Step-by-step explanation:

When the side lengths are consecutive integers, only the lengths 3, 4, and 5 will form a right triangle.

  8^2 ≠ 6^2 + 7^2 . . . . for a right triangle, the square of the hypotenuse must be the sum of the squares of the legs

  64 ≠ 36 + 49 = 85

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

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step-by-step explanation: