Question 1166715
let L = length and W = width.


your formula for the area of a rectangle is:
A = L * W


when A = 24, this formula becomes:
24 = L * W


when L is 4 cm less and W is 1 cm more, the formula becomes:
24 = (L - 4) * (W + 1)


you need to solve these two formulas simultaneously.


from the first equation, solve for L to get:
L = 24 / W


in the second equation, replace L with W / 24 to get:
(24 / W - 4) * (W + 1) = 24
simplify this formula to get:
(24 / W * W) + (24 / W * 1) - (4 * W) - (4 * 1) = 24
simplify to get:
24 + 24 / W - 4 * W - 4 = 24
combine like terms to get:
24 / W - 4 * W + 20 = 24
subtract 20 from both sides of this equation to get:
24 / W - 4 * W = 4
multiply both sides of this equation by W to get:
24 - 4 * W ^ 2 = 4 * W
subtract the left side of this equation from both sides of this equation and simplify to get:
0 = 4 * W - 24 + 4 * W ^ 2
switch sides in this equation and order the terms in descending order of degree to get:
4 * W^2 + 4 * W - 24 = 0
divide both sides of this equation by 4 to get:
W^2 + W - 6 = 0
factor this equation to get:
(W - 2) * (W + 3) = 0
solve for W to get:
W = 2 or W = -3
W can't be negative, so:
W = 2


in the first equation of L * W = 24, replace W with 2 to get:
L * 2 = 24
solve for L to get:
L = 12


you have:
L = 12 and W = 2


in your first original equation, L * W = 24 becomes 12 * 2 = 24.
since this is true, it confirms the values for L and W are good in the first equation.


in your second original equation, (L - 4) * (W + 1) = 24 becomes (12 - 4) * (2 + 1) = 24 which becomes 8 * 3 = 24.
since this is true, it confirms the values for L and W are good in the second equation as well.


your solution is that the length and width of the first rectangle is 12 cm for the length and 4 cm for the width.


breadth and width mean the same thing in this problem.