College Algebra 2

Question

A rectangular sandbox is surrounded on all sides by a strip of grass that is 4 feet wide on all sides. The length of the sandbox is 2 feet more than the width, and the total area for the sandbox and the grass is 142 square feet. Find the dimensions of the sandbox.

Answer 1

Assuming no typos in the problem...

 

the dimensions of the sandbox are x and x+2

the dimensions of the larger rectangle are (x+4+4) and ([x+2]+4+4)

(x+8)(x+10)=142

x²+18x+80=142

x²+18x+80-142=0

x²+18x-62=0

using the quadratic equation...

(-18+√324+248)/2

(-18+√572)/2

(-18+2√143)/2

-9+√143

x=-9+√143

x+2=-7+√143

-9+√143 and -7+√143 are the dimensions of the rectangular sandbox

if you want decimals you get -9+11.958=2.958 and -7+11.958=4.958

check:the dimensions of the larger rectangle with the border of grass is 8-9+√143=-1+√143

and 8-7+√143=1+√143

as decimals, the dimensions are -1+11.958=10.958 and 1+11.958=12.958

(10.958)(12.958)=141.99 square feet, and...

(-1+√143)(1+√143)=-1+143=142 square feet