Question

kim is working on picking sizes for a new rectangular banner for her school. she wants to increase the dimensions of the banners used last year using a scale factor. kim records the original length, original width, and new length for her three choices.
identify which banners have a new width of 7 feet.
select the correct answer in each row.
original length: 3 feet
original width: 4 feet
new length: 5.25 feet
original length: 5 feet
original width: 3 feet
new length: 12.5 feet
original length: 4 feet
original width: 2 feet
new length: 14 feet
has a new width of 7 feet
does not have a new width of 7 feet

Explanation:

Step1: Calculate scale factor for each banner

The scale factor \(k\) is given by the formula \(k=\frac{\text{new width}}{\text{original width}}\).

• For the first banner: Original width \(w_1 = 4\) feet, new width \(W_1=7\) feet. Scale factor \(k_1=\frac{7}{4}=1.75\). Then new length \(L_1=\text{original length}\times k_1\). Original length \(l_1 = 3\) feet. So \(L_1=3\times1.75 = 5.25\) feet.
• For the second banner: Original width \(w_2 = 3\) feet, new width \(W_2 = 7\) feet. Scale factor \(k_2=\frac{7}{3}\approx2.33\). Original length \(l_2=5\) feet. New length \(L_2 = 5\times\frac{7}{3}=\frac{35}{3}\approx11.67

eq12.5\) feet.

• For the third banner: Original width \(w_3=2\) feet, new width \(W_3 = 7\) feet. Scale factor \(k_3=\frac{7}{2}=3.5\). Original length \(l_3 = 4\) feet. New length \(L_3=4\times3.5=14\) feet.

Answer:

• Original Length: 3 feet, Original Width: 4 feet, New Length: 5.25 feet: Has a new width of 7 feet.
• Original Length: 5 feet, Original Width: 3 feet, New Length: 12.5 feet: Does not have a new width of 7 feet.
• Original Length: 4 feet, Original Width: 2 feet, New Length: 14 feet: Has a new width of 7 feet.