Question

A farmer has 300 feet of fence available to

enclose a 4500 square foot region in the

shape of adjoining squares, with sides of

length x and y. The big square has sides of

length x and the small square has sides of

length y. Find x and y.

UUUULTTUUL

x= ? feet

y = ? feet

Answer 1

Given :

A farmer has 300 feet of fence available to  enclose a 4500 square foot region in the  shape of adjoining squares, with sides of  length x and y.

The big square has sides of  length x and the small square has sides of   length y.

To Find :

The value of x and y.

Solution :

From attached figure perimeter is given by :

x + x + x + y + y + y + ( x-y ) = 300 ft

4x + 2y = 300

2x + y = 150  ...1)

Now, area is given by :

A = x² + y²

x² + y² = 4500  ...2)

Putting value of y in equation 2), we get :

$x^2 + ( 150 - 2x)^2 =4500\\\\x^2 + 4x^2 + 22500-600x =4500\\\\5x^2 -600x + 18000=0\\\\x^2 - 120x +3600=0\\\\x^2-2\times x\times 60 + 60^2 =0\\\\(x-60)^2 =0\\\\x = 60\ ft$

y = 150 - ( 2× 60 )

y = 30 ft

Therefore, the value of x and y is 60 ft and 30 ft respectively.