Question 876273
let l be length of fish pond, w be the width of fish pond, A = area of fish pond and y is width of the tile path all the way round, then
l + y = 10
w + y = 14
l * w = 24
A) w = 24/l
24/l + y = 14
y = 14 - 24/l
l + 14 - 24/l = 10
multiply both sides of = by l
l^2 + 14l - 24 = 10l
l^2 + 4l - 24 = 0
l = (-b + square root(b^2 -4ac))/2a = (-4 + square root(16 - 4*1*-24)) / 2*1 = 3.29
l = (-b + square root(b^2 -4ac))/2a = (-4 - square root(16 - 4*1*-24)) / 2*1 = -7.29
B) l = 24/w, then
24/w + y = 10
y = 10 - 24/w
w + (10 - 24/w) = 14
w + 10 - 24/w = 14
multiply both sides of = by w
w^2 + 10w -24 = 14w
w^2 - 4w -24 = 0
w = (-b + square root(b^2 -4ac))/2a = (4 + square root(16 - 4*1*-24)) / 2*1 = 7.29
w = (-b + square root(b^2 -4ac))/2a = (4 - square root(16 - 4*1*-24)) / 2*1 = -3.29
we chose the positive values for l and w
l = 3.29, w = 7.29
C) A = l * w = 24
A = 3.29 * 7.29 = 23.98 approx 24