Answer:
the width of the picture frame is, 32 cm
Step-by-step explanation:
Perimeter(P) of a rectangle is given by:
[tex]P=2(l+w)[/tex]
where,
l is the length and w is the width of the rectangle.
As per the statement:
A picture frame has a perimeter of 100 cm.
Since, the picture frame is in the form of rectangle
⇒P = 100 cm
It is given that the width is 4 cm less than twice its length
⇒[tex]w = 2l -4[/tex]
Substitute these in [1] we have;'
[tex]100 = 2(l +2l-4)[/tex]
Combine like terms;
[tex]100=2(3l-4)[/tex]
Divide by 2 to both sides we have;
[tex]50 = 3l-4[/tex]
Add 4 to both sides we have;
54 = 3l
Divide both sides by 3 we have;
18 = l
or
[tex]l = 18 cm[/tex]
Substitute this in [tex]w = 2l -4[/tex] to get w;
[tex]w = 2(18) -4[/tex]
⇒[tex]w =36-4[/tex]
[tex]w = 32 cm[/tex]
Therefore, the width of the picture frame is, 32 cm
