SOLUTION: Please help me to solve these 2 problems. Thank you very much professor. A rectangular garden has dimensions of 16 feet by 13 feet. A gravel path of equal width is to be built

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me to solve these 2 problems. Thank you very much professor. A rectangular garden has dimensions of 16 feet by 13 feet. A gravel path of equal width is to be built      Log On


   

Question 18614: Please help me to solve these 2 problems. Thank you very much professor.

A rectangular garden has dimensions of 16 feet by 13 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 492 square feet?
Thanks professor.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
l=16 feet ....b= 13 feet...let the width of the path be =w
we shall assume the path is to be laid around the garden OUTSIDE THE GARDEN AS THE GRAVEL AREA IS MORE THAN THAT OF THE GARDEN.so if the path is out-side , the rectangle remaining after the path is laid will have 16+w+w=16+2w in length and 13+w+w=13+2w in width .we get the area of path by subtracting from this the area of garden excluding the path =16*13=208
so we have (16+2w)(13+2w)-208=492
169+32w+26w+4w^2=492+208=700
4w^2+58w-531=0
now solve this using
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
BUT I THINK YOUR NUMBERS ARE WRONG ..THE AREA OF THE PATH SHOULD BE MUCH SMALLER THAN THAT OF THE GARDEN IN MY OPINION...CHECK THE NUMBERS AGAIN AND COME BACK .IF THE NUMBERS ARE O.K. FIND THE ANSWER FROM ABOVE FORMULA