Perimeter of similar triangles

The total distance around a shape is referred to as its perimeter. Depending on the dimensions, the perimeter of different shapes can be equal.

Similar figures are the figures that have the same shape but a different size. Since similar figures are related to each other, there exists a relation between their area and perimeter as well. Here we will learn to use this relation to find the unknown quantities of the figure. Read More Read Less. When two figures have the same shape but differ in size, they are said to be similar figures. In other words, two figures are said to be similar if they share many of the same characteristics but are not identical. The scale factor is the constant by which the size of a shape is increased or decreased.

Perimeter of similar triangles

The ratio of perimeters of two similar triangles is equal to the ratio of their corresponding sides. Last updated on Feb 13, Get Started. SSC Exams. Banking Exams. Teaching Exams. Civil Services Exam. Railways Exams. Engineering Recruitment Exams. Defence Exams. State Govt. Police Exams. Insurance Exams. Nursing Exams. Other Govt.

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When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. It is then said that the scale factor of these two similar triangles is 2 : 1. When you compare the ratios of the perimeters of these similar triangles, you also get 2 : 1. This leads to the following theorem. Theorem If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b. Figure 3 shows two similar right triangles whose scale factor is 2 : 3.

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. It is then said that the scale factor of these two similar triangles is 2 : 1. When you compare the ratios of the perimeters of these similar triangles, you also get 2 : 1. This leads to the following theorem. Theorem If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b. Figure 3 shows two similar right triangles whose scale factor is 2 : 3. You can now find the area of each triangle. Figure 3 Finding the areas of similar right triangles whose scale factor is 2 : 3. Theorem If two similar triangles have a scale factor of a : b , then the ratio of their areas is a 2 : b 2. Figure 4 Using the scale factor to determine the relationship between the areas of similar triangles.

Perimeter of similar triangles

Ratio of the areas is the square of the scale factor; ratio of perimeters is the scale factor. Polygons are similar when their corresponding angles are equal and their corresponding sides are in the same proportion. Just as their corresponding sides are in the same proportion, perimeters and areas of similar polygons have a special relationship. Perimeters: The ratio of the perimeters is the same as the scale factor. In fact, the ratio of any part of two similar shapes diagonals, medians, midsegments, altitudes, etc. You square the ratio because area is a two-dimensional measurement. What if you were given two similar triangles and told what the scale factor of their sides was? How could you find the ratio of their perimeters and the ratio of their areas? The two rectangles below are similar. Find the scale factor and the ratio of the perimeters and verify that the two results are the same.

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The scale factor is the constant by which the size of a shape is increased or decreased. Odisha Junior Teacher. Odisha RI. Haryana Police Commando. BEL Probationary Engineer. BSF Head Constable. Odisha Amin. Example 1: Determine the perimeters of the shapes given below and determine the ratio of perimeters of the below shapes. UP Police Head Operator. IB MTS. SSC Selection Post. Maharashtra Zilla Parishad Health Supervisor. HP SET. Patna Civil Court Peon.

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Judiciary Exams. Tripura TET. MP Police SI. State Govt. Patna Civil Court Group C. Telangana High Court Process Server. Delhi Police Head Constable. The Relation between the Perimeter of the sides of Similar Figures. CIL MT. Find the area of each triangle. Nainital Bank. Maharashtra Nagar Parishad Accountant.