https://file.aiquickdraw.com/mathbot/file/1725378667326maakwp1e.jpg

Let's analyze the problem step by step.

### Problem Recap:
We are given a triangle \( A \) with an area of 7.5 square units. A scaled copy of this triangle was created, and we need to answer the following questions:

1. **How many times larger is the area of the scaled copy compared to that of Triangle \( A \)?**
2. **What scale factor did Lin apply to Triangle \( A \) to create the copy?**
3. **What is the length of the bottom side of the scaled copy?**

### Step-by-Step Solution:

#### a. How many times larger is the area of the scaled copy compared to that of Triangle \( A \)?

Let the area of the scaled copy be denoted as \( A_{\text{scaled}} \). The problem is asking for the ratio of the areas, which is:

\[
\text{Ratio of areas} = \frac{A_{\text{scaled}}}{A}
\]

From the given information, we don't know the area of the scaled copy yet, so we cannot compute this ratio directly. We need more information to determine this.

#### b. What scale factor did Lin apply to the Triangle \( A \) to create the copy?

The scale factor \( k \) applied to the sides of a geometric figure results in the area being scaled by \( k^2 \). To find the scale factor, we would use:

\[
k = \sqrt{\frac{A_{\text{scaled}}}{A}}
\]

However, to find the scale factor, we need the area of the scaled triangle, which again we do not have yet.

#### c. What is the length of the bottom side of the scaled copy?

The length of any side in the scaled triangle is related to the original length by the scale factor \( k \). So if the original bottom side length is \( l \), then the length of the bottom side in the scaled triangle is:

\[
\text{Length of the bottom side in scaled triangle} = l \times k
\]

### Additional Information from the Image:
The grid in the image might help us estimate the original triangle's dimensions (base and height). Using this information, we can then calculate the scale factor and solve the above questions.

Would you like to proceed with calculating these using the dimensions estimated from the grid in the image? Or do you have any further details that can help solve the problem more precisely?

Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 7.5 square units.

 a. How many times larger is the area of the scaled copy compared to that of Triangle A?
 b. What scale factor did Lin apply to the Triangle A to create the copy?
 c. What is the length of the bottom side of the scaled copy?

Learn how to solve a geometry problem involving scaling and area ratios with Triangle A. Discover how to calculate the scale factor and determine the dimensions of the scaled copy. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation