Question

A triangle has side lengths of (2u-4v)(2u−4v) centimeters, (10u+2w)(10u+2w) centimeters, and (w-7v)(w−7v) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

Answer:

          $\bold{104u^2+65v^2+5w^2-16uv+40uw-14vw}$

Step-by-step explanation:

Perimeter of the triangle is the sum of its side lengths.

$(2u-4v)(2u-4v)+ (10u+2w)(10u+2w)+ (w-7v)(w-7v)=\\\\= (2u)^2-2\cdot2u\cdot4v+(4v)^2\ +\ (10u)^2+2\cdot10u\cdot2w+(2w)^2\ +\ \\\\{}\qquad\qquad\qquad \qquad\qquad\qquad\qquad\qquad\quad +w^2-2\cdot w\cdot7v+(7v)^2=\\\\=4u^2-16uv+16v^2+100u^2+40uw+4w^2+w^2-14wv+49v^2 =\\\\=104u^2+65v^2+5w^2-16uv+40uw-14vw$

Answer 2

Answer:

3w−11v+12u

Step-by-step explanation:

2u−4v+10u+2w+w−7v

2u-4v+10u+2w+1w-7v

2u−4v+10u+2w+1w−7v

2u+10u−4v−7v+2w+1w

2u+10u −4v−7v +2w+1w

^12u         ^-11v     ^3w

12u -11v+3w

3w−11v+12u

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