Answer:
The rectangle is 13cm by 11cm (or 11cm by 13cm)
Step-by-step explanation:
Length plus width = 25
L+W = 24
Area is 143
A = LW
143 = LW
We have two equations and two unknowns
L+W = 24 Solve for W by subtracting L from each side W = 24-L
143 = LW
Now substitute into the second equation
143 = L(24-L)
Distribute
143 = 24L - L^2
Multiply by -1
-143 = -24L +L^2
-143 = L^2 -24L
Completing the square
-24/2 = -12 -12^2 =144
Add 144 to each side
-143+144 = L^2 -24L+144
1 = (L-12)^2
Take the square root of each side
±sqrt(1) = sqrt( (L-12)^2)
±sqrt(1) = (L-12)
Add 12 to each side
12±sqrt(1) = (L-12)+12
12±1 = L
13=L or 11=L
Now we need to find W
W = 24 - L
W = 24-13 W = 24-11
W = 11 or W =13
