Respuesta :
ANSWER
• W = 10
,• L = 16
EXPLANATION
Let W be the width of the rectangle and L the length. We know that "the length is 4 less than twice the width" which translates as:
[tex]L=2W-4[/tex]The perimeter, which is 52, is twice the length plus twice the width:
[tex]52=2L+2W[/tex]We have two equations with two variables. We can use the substitution method to solve the system. Replace the first equation of L as a function of W in the second equation:
[tex]52=2(2W-4)+2W[/tex]And solve for W. First we have to apply the distributive property to the parenthesis expression:
[tex]\begin{gathered} 52=2\cdot2W-2\cdot4+2W \\ 52=4W-8+2W \end{gathered}[/tex]Then we add like terms:
[tex]\begin{gathered} 52=(4W+2W)-8 \\ 52=6W-8 \end{gathered}[/tex]Add 8 on both sides of the equation:
[tex]\begin{gathered} 52+8=6W-8+8 \\ 60=6W \end{gathered}[/tex]And divide both sides by 6:
[tex]\begin{gathered} \frac{60}{6}=\frac{6W}{6} \\ 10=W \end{gathered}[/tex]Now we have that W = 10. Replace this value in the first equation we had to find L:
[tex]\begin{gathered} L=2\cdot10-4 \\ L=20-4 \\ L=16 \end{gathered}[/tex]So L = 16
