Answer:
the dimensions of the swimming pool are 5 cm by 7 cm
Explanation:
the 5 and 7 are interchangeable because, when multiplied they give 35 and when doubled and added they give 24
we can use these formulas to solve:
A = lw (Area formula)
P = 2l + 2w (Perimeter formula)
we can solve the area formula for 'l' and have: l = 35/w
we can substitute '35/w' for 'l' in the perimeter formula to get:
2(35/w) + 2w = 24
70/w + 2w = 24
we can multiply each side by 'w' to eliminate it as a denominator:
70 + 2w² = 24w
we now have this quadratic formula:
2w² -24w + 70 = 0
if we divide each term by 2 we get:
w² - 12w + 35 = 0
we can graph this or 'unfoil' it and get (w-5)(w-7) = 0
this means the length and width, or width and length, are 5 and 7