Find each missing length to the nearest tenth 6^2+3^2=c^2

If you compute the squares and sum them, the equation becomes

In order to solve for , you need the extract the square root from both sides:

Please note that if this problem is about the lengths of the sides of a triangle, you can only accept the positive solution, since it wouldn't make any sense to consider a side with negative length.

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