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?
3
18 cm
32 cm
0 48 cm
0 50 cm

Answer 1

The correct answer is option 2: 32 cm

Explanation:

Let l be the length of the picture frame and w be the width

Then according to given statements, the system of equations will be

`2l+2w = 100\ \ \ Eqn\ 1\\w = 2l-4\ \ \ Eqn\ 2`

Putting w = 2l-4 in equation 1

`2l+2(2l-4) = 100\\2l+4l-8=100\\6l-8 = 100\\6l = 100+8\\6l=108\\(6l)/(6)=(108)/(6)\\l = 18`

Putting the value of l in equation 2

`w = 2(18)-4\\w = 36-4\\w = 32`

The width is 32 cm

Hence,

The correct answer is option 2: 32 cm