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

Answer 1

Answer:

The correct answer is option 2: 32 cm

Step-by-step 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

$2l+2(2l-4) = 100\\2l+4l-8=100\\6l-8 = 100\\6l = 100+8\\6l=108\\\frac{6l}{6}=\frac{108}{6}\\l = 18$

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