Question 275915
The length of a rectangle is 2 cm more than three times the width.
 Find the dimensions of this rectangle if the area is 21 cm^2. 
:
There is, and it's pretty easy
:
Write an equation for each statement
"The length of a rectangle is 2 cm more than three times the width."
L = 3W + 2
and
" the area is 21 cm^2. "
L * W = 21
:
Replace L with (3W+2) from the 1st statement
(3W + 2) * W = 21
3W^2 + 2W - 21 = 0
A quadratic equation we can factor
(3W - 7)(W + 3) = 0
The positive solution
3W = 7
W = {{{7/3}}}
W = 2{{{1/3}}} is the width
:
Find the length using L = 3W + 2
L = 3({{{7/3}}}) + 2
L = 7 + 2
L = 9
;
:
Check solutions by finding the area
9 * {{{7/3}}} = 21