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The sides of a triangle measure 9.12 and 15 inches. Find the sides of a similar triangle if the side corresponding to the 1 finch side of the given triangle is 5 inches.

$$3,4,5$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 9

Elements of Geometry

Derivatives

Baylor University

Idaho State University

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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for this problem. We have two triangles were told that one is larger. Mm. Make that a straight line there. One is larger and one is smaller. But our goal is to see how these are related. Now we're told that they're similar. What do similar triangles. What does that mean? We say two triangles are similar. Well, what that means. And I'm going to use some numbers just for an example. Before I put in our real numbers here. If I know for example, let's say that these sides are one and two. If I'm told that the Big Triangle is similar, it means that as I grow this side let's say I multiply it by 10 and I have 10 there. This side is going to grow at the same proportion multiplied one times 10 and we're multiplying two times 10. That's how similar triangles work. So let's look at our specific case. What do I know? Well, we're told that the Big Triangle has sides measuring nine, 12 and 15. Okay, so I know all three sides with my bigger triangle for the small triangle. We're told that the side that compares to the 15 inch side is five inches, so I'm just going to mark these. So that side the two red sites correspond 15 to 5. Help. What about these green sides? Well, how did I go from 15 to 5? It looks like I divided by three. So I'm gonna take 12 and divide by three. And that's going to give me a four. Okay. What about the third side? It's blue. Well, again, if I'm dividing by 39 divided by three is going to be three. So you can see this if I compare these sides big to small 93 big to small, 15 to 5. Big to small, 12 to 4. In each case, all of these fractions reduce the same fraction one third. So all of the sides keep that same proportion as we go from one triangle to the other. So our new triangle has the sides of 34 and five

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