Question 165844
Three times the width of a certain rectangle exceeds twice its length by three inches, and four times its length is twelve more than its perimeter. Find the dimensions of the rectangle. 
:
Take it step-by-step, write an equation each statement:
:
"Three times the width of a certain rectangle exceeds twice its length by three inches,"
3W = 2L + 3
:
" four times its length is twelve more than its perimeter."
4L = 12 + (2L+2W)
4L = 12 + 2L + 2W
4L - 2L = 12 + 2W
2L = 12 + 2W
Simplify divide by 2
L = W + 6
:
In the 1st equation (3W = 2L+3) substitute (W+6) for L
3W = 2(W+6) + 3
3W = 2W + 12 + 3
3W - 2W = 15
W = 15
:
Find L
L = 15 + 6
L = 21
:
:
See if this is true in statement:
"Three times the width of a certain rectangle exceeds twice its length by three"
3(15) = 2(21) + 3
45 = 42 + 3
:
See if you can prove it in the statement:
"four times its length is twelve more than its perimeter."
:
:
Did the explain it clearly to you? Let me know.