Question 160048
The perimeter of a cross section of a "two-by-four" piece of lumber is 10 1/2 in. The length is twice the width. Find the actual dimension of the cross section of a two-by-four.
:
You're right on the last equation 2(2n+n) = 10.5.
Let n = the width
"length is twice the width
2n = length
:
Perimeter is:
2L + 2W = 10.5
Replace L with 2n and W with n
2(2n) + 2(n) = 10.5
4n + 2n = 10.5
6n = 10.5
n = {{{10.5/6}}}
n = 1.75" is the width, and 2(1.75) = 3.5" is the length
or
1{{{3/4}}} by 3{{{1/2}}} if you prefer