What are the dimensions of a lake?

Question

An artificial lake is in the shape of a rectangule and has an area of 9/20 square mile. The width of the lake is 1/5 the length of the lake. What are the dimensions of the lake?

Answer 1

When dealing with a problem like this it is important to state what you know.  You know that Area is 9/20 (in math notation: A=9/20) and that the width (W) is 1/5 the length (L) - (W=1/5*L).  You also need to remember the formula for the area of a rectangle (A=LW).

 

So, A=L*1/5*L

 

=L*L (or L^2) / 5

 

(L^2)/5=9/20

 

L^2=45/20  (multiply both sides by 5)

 

L^2=9/4  (reduce by dividing both numerator and denominator by 5)

 

L=3/2  (solve by taking the square root of both sides => square root of 9 is 3, square root of 4 is 2)

 

W=L/5=(3/2)/5=3/10

 

Check by multiplying (3/2)*(3/10) = 9/20

Answer 2

Say, length =x mile

Width =.  x/5 mile

x*x/5=9/20

20x*x=45

x*x=45/20

      =9/4

x=3/2 mile

Length =3/2 miles

Width=. 3/10 miles