A rectangle is similar to another rectangle with dimensions 8 cm by 12 cm. If the shorter side of the similar rectangle is 6 cm, what is its longer side?

Question

Question 4 options:

8 cm

9 cm

10 cm

12 cm

Answer 1

To find the longer side of the similar rectangle, we can use the property of similar rectangles that their corresponding sides are in proportion.

Given:

• Dimensions of the original rectangle: 8 cm (shorter side) and 12 cm (longer side).
• Shorter side of the similar rectangle: 6 cm.

Let's denote:

• The longer side of the similar rectangle as \( x \).

Since the rectangles are similar, we can set up a proportion between the sides of the rectangles:

\[ \frac{\text{shorter side of similar rectangle}}{\text{shorter side of original rectangle}} = \frac{\text{longer side of similar rectangle}}{\text{longer side of original rectangle}} \]

This can be written as:

\[ \frac{6}{8} = \frac{x}{12} \]

Now, we can cross-multiply to solve for \( x \):

\[ 6 \times 12 = 8 \times x \]

\[ 72 = 8x \]

Now, divide both sides by 8:

\[ x = \frac{72}{8} = 9 \]

Thus, the longer side of the similar rectangle is \( 9 \) cm.

The answer is 9 cm.