Length, Width - Solution / Explanation

[Guest]

A rectangular park is enclosed by a walkway 4 yards wide.

Park- 15200 square yards.

Walkway - 2104 square yards.

Determine length and width of park.

Let x = length of park.

15200 / x = width of park.

(x + 4)(15200 / x + = ( 15200 + 2104) = 17304 **

8x + 121600 / x + 15264 = 17304 **

8x^2 - 2040x = 121600 **

x^2 - 255x = 15200

x = 127 * 5 + - 32 * 5 = 160 or 95

length of park = 160 or 95

width = 15200 / 160 = 95 or 15200 / 95 = 160

** I don't understand these steps.

Also, can you provide some hints/tips about quadratics ? I am not very good at these.

[Guest]

As usual the facts presented in the question are not all that clear

The park is enclosed by a walkway so I will assume the walkway area is not included in the park area as it is outside and encloses it.

Let L = length of the park
Let W = width of the park

Area of the park.... LW = 15200 square yards.......eqn1

Area of the walkway.... (2 x 4 x (L + ) + (2 x 4 x W) = 2104 square yards

This gives....... 8L + 64 + 8W = 2104 sq yards

This gives....... 8L + 8W = 2104 - 64

This gives......... L + W = 255 OR L = 255 - W .............eqn2

Substitute eqn2 in eqn1 gives W(255 - W) = 15200

Which gives -W^2 + 255W - 15200 = 0

divide by -1 gives........ W^2 - 255W + 15200 = 0

solve for W using formulae.....

(255 +or- sqroot( 255^2 - (4 x 1 x 15200)) / 2

(255 +or- sqroot(65025 - 60800)) /2

(255 + 65) / 2 OR (255 - 65) / 2

160 OR 95

Both roots are real and positive

160 yards is the length of the park
95 yards is the width of the park

160 + 95 = 255 yards

160 x 95 = 15200 square yards

[Guest]

Can you provide some hints/tips about quadratics ?

[Guest]

There are lots of examples on this forum and other web pages.
Quadratics are of the form Ax^2 + Bx + C = 0
The question is to solve for x.
Can be solved by....
Factorising....
Completing the Square.....
Using the formulae....

You need to try examples yourself then ask questions.