Answer:
the width of the picture frame is, 32 cm
Step-by-step explanation:
Perimeter(P) of a rectangle is given by:
\(P=2(l+w)\)
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
⇒\(w = 2l -4\)
Substitute these in [1] we have;'
\(100 = 2(l +2l-4)\)
Combine like terms;
\(100=2(3l-4)\)
Divide by 2 to both sides we have;
\(50 = 3l-4\)
Add 4 to both sides we have;
54 = 3l
Divide both sides by 3 we have;
18 = l
or
\(l = 18 cm\)
Substitute this in \(w = 2l -4\) to get w;
\(w = 2(18) -4\)
⇒\(w =36-4\)
\(w = 32 cm\)
Therefore, the width of the picture frame is, 32 cm
