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

the width of the picture frame is, 32 cm

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.