The corresponding sides of similar figures are 10 and 25. What is the ratio of their areas?
Answers
Geometry
Similar Triangles: Perimeters and Areas
Similar Triangles: Perimeters and Areas
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1, Δ ABC∼ Δ DEF.
Figure 1 Similar triangles whose scale factor is 2 : 1.
The ratios of corresponding sides are 6/3, 8/4, 10/5. These all reduce to 2/1. It is then said that the scale factor of these two similar triangles is 2 : 1.
The perimeter of Δ ABC is 24 inches, and the perimeter of Δ DEF is 12 inches. When you compare the ratios of the perimeters of these similar triangles, you also get 2 : 1. This leads to the following theorem.
Theorem 60: If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b.
Example 1: In Figure 2, Δ ABC∼ Δ DEF. Find the perimeter of Δ DEF
Figure 2 Perimeter of similar triangles.
Figure 3 shows two similar right triangles whose scale factor is 2 : 3. Because GH ⊥ GI and JK ⊥ JL , they can be considered base and height for each triangle. You can now find the area of each triangle.
Figure 3 Finding the areas of similar right triangles whose scale factor is 2 : 3.
Now you can compare the ratio of the areas of these similar triangles.
This leads to the following theorem:
Theorem 61: If two similar triangles have a scale factor of a : b, then the ratio of their areas is a2 : b2.
Hey there!
Is that triangles u r talking about?
Ratio of areas of similar triangles is equal to the square of the ratio of sides.
Thus the required ratio is 100/625=4/25
4:25