5. Here is a shape with some measurements in cm.

Answer:

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Step-by-step explanation:

The table is completed below.

We can say that the relationship between the scale factor and the area of scaled copies is proportional.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Using the formula for the area of a triangle:

Area = 1/2 x base x height

With a base of 3cm and height of 2cm, the area of the original triangle is:

Area = 1/2 x 3cm x 2cm = 3cm²

To find the area of the scaled triangles, we can use the scale factor to determine the corresponding dimensions, and then calculate the area using the same formula.

Scale factor Corresponding dimensions Area

1                         3cm x 2cm               3cm²

2                         6cm x 4cm                12cm²

5                        15cm x 10cm               75cm²

s                        3s cm x 2s cm             3s² cm²

Now,

To see if the relationship between the scale factor and the area of scaled copies is proportional, we can calculate the ratio of the area to the scale factor for each row of the table:

Scale factor Corresponding dimensions Area Ratio of area to scale factor

1                             3cm x 2cm             3cm²          3/1 = 3

2                             6cm x 4cm             12cm² 12/2 = 6

5                                 15cm x 10cm      75cm² 75/5 = 15

s                            3s cm x 2s cm     3s² cm²  (3s²)/s = 3s

In each case, the ratio of the area to the scale factor is constant, which means that the relationship between the scale factor and the area of scaled copies is indeed proportional.

Therefore,

We can say that the relationship between the scale factor and the area of scaled copies is proportional.

Learn more about triangles here:

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