Question

A rectangular gardan is surrounded by a walk of uniform width. The area of the garden is 200 square yards. If the dimensions of the garden plus the walkway are 18 yards by 26 yards, find the dimensions of the garden.

***NOTE*** This is a Quadratic Word Problem, so please use the Quadratic Method when solving and show all steps!!

Answer 1

Answer:
`6√(6)+4 * 6√(6)-4` yards

Explanation:

Let the length of the walkway be x yards. Then,

`(18-2x)(26-2x)=200\\\\4x^2 -88x+468=200\\\\4x^2-88x+268=0\\\\x^2 -22x+77=0\\\\x=(22 \pm √(22^2 -4(77)))/(2)\\\\=11 \pm 3√(6)`

However,
`x=11+3√(6) > 18`, which is illogical, so we take
`x=11-3√(6)`.

So,

`18-2x=18-2(11-3√(6))=6√(6)-4\\\\26-2x=26-2(11-3√(6))=4+6√(6)`