Questions: Select the correct answer from each drop-down menu. A triangular piece of rubber is stretched equally from all sides, without distorting its shape, such that each side of the enlarged triangle is twice the length of the original side. The area of the triangle to times the original area.

Select the correct answer from each drop-down menu.

A triangular piece of rubber is stretched equally from all sides, without distorting its shape, such that each side of the enlarged triangle is twice the length of the original side.

The area of the triangle to times the original area.

Transcript text: Select the correct answer from each drop-down menu. A triangular piece of rubber is stretched equally from all sides, without distorting its shape, such that each side of the enlarged triangle is twice the length of the original side. The area of the triangle $\square$ to $\square$ times the original area.

Solution

Solution Steps

To determine how the area of the triangle changes when each side is doubled, we can use the properties of similar triangles. When the sides of a triangle are scaled by a factor, the area is scaled by the square of that factor.

Solution Approach

Identify the scaling factor for the sides of the triangle.
Calculate the scaling factor for the area by squaring the side scaling factor.

Step 1: Identify the Scaling Factor

The sides of the triangle are stretched equally, resulting in a scaling factor of $ k = 2 $.

Step 2: Calculate the Area Scaling Factor

The area of a triangle scales with the square of the side length scaling factor. Therefore, the area scaling factor is given by: \[ \text{Area Scaling Factor} = k^2 = 2^2 = 4 \]