Question

1. if a rectangle with an area of 42 square cm, and length 7 cm, is copied using scale factor 3. what are the measurements of the new rectangle and its area?

new length
new width
area

Explanation:

Step1: Find the original width

We know that the area of a rectangle $A = l\times w$. Given $A = 42$ cm² and $l = 7$ cm. So, $w=\frac{A}{l}=\frac{42}{7}=6$ cm.

Step2: Find the new length and width

If the scale - factor is $3$ (assuming the scale - factor is missing and we take it as 3 for the sake of solution. If it is a different value, the following steps can be adjusted accordingly). The new length $l_{new}=l\times k$, where $k$ is the scale - factor. So, $l_{new}=7\times3 = 21$ cm. The new width $w_{new}=w\times k=6\times3 = 18$ cm.

Step3: Find the new area

The new area $A_{new}=l_{new}\times w_{new}=21\times18 = 378$ cm².

Answer:

New length: 21 cm
New width: 18 cm
Area: 378 cm²