Question

the scale factor of each model is 1:12. find the missing dimensions.

1. lamp height: height: 1\frac{1}{3} in.
2. couch height: 32 in. height:

length: 69 in. length:

1. table height: height: 6.25 cm

width: width: 11.75 cm
length: length: 20 cm

Explanation:

Step1: Find the actual height of the lamp

The scale factor is \(1:12\), which means actual dimension \(=\) model dimension\(\times12\).
The model height of the lamp is \(1\frac{1}{3}=\frac{4}{3}\) in.
Actual height \(=\frac{4}{3}\times12\)
\(=\frac{4\times12}{3}=16\) in.

Step2: Find the model dimensions of the couch

Model dimension \(=\) actual dimension\(\div12\)
For height: Actual height \( = 32\) in. Model height \(=32\div12=\frac{32}{12}=\frac{8}{3}=2\frac{2}{3}\) in.
For length: Actual length \(=69\) in. Model length \(=69\div12=\frac{69}{12}=\frac{23}{4} = 5.75\) in.

Step3: Find the actual dimensions of the table

Actual dimension \(=\) model dimension\(\times12\)
For height: Model height \(=6.25\) cm. Actual height \(=6.25\times12 = 75\) cm.
For width: Model width \(=11.75\) cm. Actual width \(=11.75\times12=141\) cm.
For length: Model length \(=20\) cm. Actual length \(=20\times12 = 240\) cm.

Answer:

1. Actual height of lamp: \(16\) in.
2. Model height of couch: \(2\frac{2}{3}\) in, model length of couch: \(5.75\) in.
3. Actual height of table: \(75\) cm, actual width of table: \(141\) cm, actual length of table: \(240\) cm.