Answer :
ANSWER
height = 80in
width = 30 in
EXPLANATION
The perimeter of the door is the sum of twice the width and twice the height:
[tex]220=2w+2h[/tex]We also know that the width is 50in less than the height:
[tex]w=h-50[/tex]Replace w by this equation into the perimeter:
[tex]220=2(h-50)+2h[/tex]Solve for h. Apply distributive property:
[tex]220=2h-100+2h[/tex]Add like terms:
[tex]220=4h-100[/tex]Add 100 to both sides of the equation
[tex]\begin{gathered} 220+100=4h-100+100 \\ 320=4h \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} \frac{320}{4}=\frac{4h}{4} \\ 80=h \end{gathered}[/tex]The height of the door is 80 in.
Now replace h = 80 into the equation of the width of the door:
[tex]w=80-50=30[/tex]The width of the door is 30 in.