The perimeter of an equilateral triangle is 99 in more than the perimeter of a? square and the side of the triangle is 55 in longer than the side of the square.

Question

Find the side of the triangle

Answer 1

Here's how I'm marking my variables:

P_t = Perimeter of triangle

P_s = Perimeter of square

S_t = Side of triangle

S_s = Side of square

 

Here's what we know:

P_t = P_s + 99 (Triangle perimeter is square's plus 99)

S_t = S_s + 55 (Triangle side is square's plus 33

S_t = P_t/3 (or P_t = 3S_t) (the triangle's side is one-third of its perimeter)

S_s = P_s/4 (or P_s = 4S_s) (the square's side is one-fourth of its perimeter)

 

P_t/3 = S_s + 55 (if S_s plus 55 is the same as P_s, then that means it's also 1-third of the entire triangle perimeter)

Multiply both sides by 3:

P_t = 3S_s + 165 = P_s + 99 (We now have P_t equal two other equations, and that means they're equal to one another as well)

Subtract 99 to both sides:

3S_s + 66 = P_s

3S_s + 66 = 4S_s (Substituting the perimeter variable with an equal variable (the square perimeter is 4 times its single side)

Subtract 3S_s to both sides:

66 = S_s

And now we know the length of the square's side.

 

S_t = 55 + 66

S_t = 121

 

Check

121 * 3 (triangle perimeter)= 66 * 4 + 99 (square perimeter)

363 = 264 + 99

363 = 363