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

Let the length be L..... then the width is 24 - L

And area = L * W  = L(24 - L)......and this equals 143

So we have

L(24-L) = 143

24L - L^2 = 143     rearranging, we have

L^2 - 24L + 143 = 0     factor

(L - 11)(L - 13) = 0  and setting each factor to 0....we have that L = 11cm or L = 13cm

And......depending upon how we orient the rectangle, the width either = 13cm or 11cm.

Let's find all the possible addition solutions for 24.

0,24

1,23

2,22

3,21

4,20

5,19

6,18

7,17

8,16

9,15

10,14

11,13

12,12

Now we multiply these until one of them equals 143

0*24=0

1*23=23

2*22=44

3*21=63

4*20=80

5*19=95

6*18=108

7*17=119

8*16=128

9*15=135

10*14=140

11*13=143

Since 11*13=143, then 11 and 13 are the width and length