What is the Length and Width of a rectangle when the area equals 19460 square feet where Length = L and Width = (5/8)L ?

Question

To find the area of a rectangle the equation is A=L*W; where A = area, L=Length, and W=Width. 

If I know that A=19,460 Ft squared and I also know that the width is 5/8 (five eighths) of the length...

How can i determine what the lengths are?

19460 = L  *  (5/8)W

 

Answer 1

Chad- 

You're close. You are correct that L * W = A, and in this case W = (5/8)L. 

Replace W in the first equation with the second, and you get

19460 = L * (5/8) L or 

19460 = (5/8) L²

Multiply each side by 8 and divide by 5 (to clear out the 5/8 on the right) to get

(8)(19460)/5 = L²

31136 = L²

L = 176.45 feet

W = 5/8 (176.45) = 110.28 ft

To check, (176.45)* (110.28)  = 19458.9  - Since we rounded out results to two places, we'll be a little off, but the result is close.