Finding the Area of a Similar Right Triangle

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Homework Help Overview

The discussion revolves around finding the area of a right triangle that is similar to another triangle, given that the hypotenuse of one triangle is twice as long as the other. Participants explore the implications of similarity in triangles, particularly focusing on the relationship between corresponding angles and side lengths.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formula for the area of a triangle and how it relates to the dimensions of similar triangles. There are questions about how the areas of the two triangles compare based on their side length ratios.

Discussion Status

The discussion is ongoing, with participants providing insights into the relationship between the areas of similar triangles and exploring the proportionality of their dimensions. Some guidance has been offered regarding the area formula and its application to similar triangles, but no consensus has been reached.

Contextual Notes

There is a focus on the assumption that the triangles are similar and the implications of this similarity on their dimensions and areas. Participants are also considering the specific case of one triangle having a hypotenuse that is twice the length of the other.

grace77
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For example: if it was given that two right triangles are similar triangles and that the hypotenuse of one is twice as long than the other how would you find the area of the triangle with the twice as long hypotenuse given the area of the other?
Similar right triangles means they are the same corresponding angle? And area of a triangle is 1/2(bxh)
Would really appreciate it if someone could point me in the right direction. Thanks
 
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Similar means the angles are congruent between the two figures, and the corresponding sides are in proportion.Imagine two similar right triangles and the sides of the bigger one are each k times the sides of the smaller one.

a=(1/2)bh, and A=(1/2)(kb)(kh).
How do a and A compare?
 
symbolipoint said:
Similar means the angles are congruent between the two figures, and the corresponding sides are in proportion.Imagine two similar right triangles and the sides of the bigger one are each k times the sides of the smaller one.

a=(1/2)bh, and A=(1/2)(kb)(kh).
How do a and A compare?
The base and height would be double due to the ratio right? Therefore the area would be 1/2(2b x2h)
 
grace77 said:
The base and height would be double due to the ratio right? Therefore the area would be 1/2(2b x2h)

For your example, yes. My discussion is general. Your example uses, "twice the lengths" but my generalization uses "k times the lengths".
 

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