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The sides of a triangle measure 5,6 and 8 inches. Find the sides of a similar triangle if the side corresponding to the 6 inch side of the given triangle is 9 inches.

$$15 / 2,9,12$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 9

Elements of Geometry

Derivatives

Oregon State University

Harvey Mudd College

University of Nottingham

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.

00:43

Find the measures of the s…

01:17

The ratio of the measures …

00:37

The lengths of two sides o…

02:11

The sides of a triangle me…

01:19

Find the perimeter of a ri…

01:43

A 6-8-10 right triangle $A…

08:37

Find the perimeter of an i…

02:45

An isosceles triangle, a t…

01:06

Find the length of the hyp…

02:21

In triangle $A B C, A=45.6…

02:14

for this problem. We are looking at two triangles. First, we have a triangle with sides 56 and eight. So I'm just going to draw ourselves a little triangle. It's not necessarily to scale, but 56 and eight. And then we're told we have a similar triangle. Now this is going to be a little bit bigger. We're told that the corresponding side to the six inch, six inches on the first triangle is nine inches on the second, and we have two other sides that we don't know A and B. So how do we find the sides on this similar triangle? Remember, a similar triangle means that I have taken my original triangle and either expanded it or shrunk it proportionately. So as I look at these, if one side was twice as big as the other in this triangle, it's still going to be twice as big as the other in this triangle, just instead of being perhaps two and four. Maybe now it's 20 and 40. So even if the sides are different proportionately, they have remained consistent. So let's take a look. I know that this red side in this red side correspond to each other and I'm just going to mark in my colors. Besides the correspond so I can set up a proportion. I can say Let's go small to big So the small triangle to the Big Triangle has a proportion of 6 to 9. Well, let's compare that to our green. Small to big would be five to a So let's solve for a I cross multiply. I get six a equals 45 and then I can divide by six. And I can simplify this a little bit the top and bottom of both, divisible by three So I can change this to 15 halves. So one of these sides would be 15 halves. Okay, what about the other side? Be well again. I know that going from the small to big is 6 to 9. Those are the sides we were given. If I look at the blue sides, eight to be would be in that same proportion. I can cross, multiply and say six b equals 72 and I can divide by six, which gives us be Equalling 12. So the three sides of our big triangle are 15 halves 12 and the one we were given, which is nine

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