Question

A picture frame has a perimeter of 100 cm. Its width is 4 cm less than twice its length. What is the width of the picture frame?

Answer 1

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

Answer 2

2l + 2w = 100
l + w = 50 . . . (1)
w = 2l - 4 . . . (2)
l + 2l - 4 = 50
3l - 4 = 50
3l = 50 + 4 = 54
l = 54/3 = 18
w = 2(18) - 4 = 36 - 4 = 32

Therefore, the width of the picture frame is 32 cm.