Question

Ashley is making 6 identical rectangular picture frames each frame is 24 cm long which is twice the width she has 5 meters of lumber how much will she have left over after making the frames?

Answer 1

The length of each frame is l = 24 cm.

The length of the frame is twice the width means,

$\begin{gathered} l=2w \\ 24=2w \\ w=12 \end{gathered}$

The formula for the perimeter of rectangle frame is,

$P=2(l+w)$

Substitute the values in the formula to obtain the perimeter of one frame.

$\begin{gathered} P=2(12+24) \\ =2\cdot36 \\ =72 \end{gathered}$

The perimeter of each rectangle is same. so perimeter of the 6 rectangle frames is,

$\begin{gathered} P^{\prime}=72\cdot6 \\ =432\text{ cm} \\ =432\text{ cm}\cdot\frac{1\text{ m}}{100\text{ cm}} \\ =4.32\text{ m} \end{gathered}$

So 4.32 meter of lumber is used for making 6 picture frames.

Determine the left over umber after making of six frames.

$\begin{gathered} l=5\text{ m -4.32 m} \\ =0.68\text{ m} \\ =0.68\text{ m}\times\frac{100\text{ cm}}{1\text{ m}} \\ =68\text{ cm} \end{gathered}$

So left over lumber is 0.68 meter or 68 centimeter.

Answer: 0.68 meter or 68 centimeter.