the length of a rectangle plus its width is 24 cm. the area is 143 square cm. what are the length and width of the rectangle?

L=13, w=11

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