equations of Radicals

Question

anitas square garden is 21 square feet larger than freds square garden. they pool their money together to buy fencing. if they need 84 feet of fence, what is the size of each garden?

Answer 1

 

A is the side measure of Anita's square garden.

F is the side measure of Fred's square garden.

 

The area of the square is the side measure times itself.

Area = s x s = s^2 where s is the measure of the side of the square.

 

Then 

 

 F*F + 21 = A*A <--- Anita's garden is 21 square feet larger

 

The perimeter of the square is 4*s, where s is the measure of the side 

of the square.

 

Together they need 84 feet of fence.

84 = 4F + 4A  <--- both perimeters are 84 feet

84 = 4(F+a) <-- factors out 4

21 = F + A

 

Now we have two equations and two unknowns, F and A.

 

 

21 = F + A

A^2 = F^2 + 21

 

Solving the first equation for F,   F = 21-A.

Substituting that into the second equation:

 

A^2 = (21-A)^2 + 21

A^2 = (441 - 42A + A^2) + 21 <-- FOIL method

 

A^2 = a^2 - 42A + 462

 

0 = -42A + 462

 

-462 = -42A

A = -462/-42

 

A = 11

 

 

So the measure of one side of Anita's garden is 11 feet.

The area of her garden is 121 square feet.

 

The area of Fred's garden is 121-21 = 100 square feet.

So the measure of one side of Fred's garden is 10 feet.

 

The perimeter of Anita's garden is 44 feet.

The perimeter of Fred's garden is 40 feet.

The total perimeter is 84 feet.