Find the unknown side lengths in each pair of similar triangles.

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Accepted Answer

Welcome back. I am so glad you're here. We're told for the following pair of similar triangles determine the value of all the unknown side lengths. We have two triangles. The first triangle, the first side has one Hashmark and that's labeled 105. Another side has two hash marks and that's labeled H A third side has three hash marks and that's labeled K for the second triangle. The first side has one Hashmark that's labeled 25. The second side with two hash marks is labeled 20. And the third side with three hash marks is labeled 15. The sides that are similar are the sites that have the same number of hash marks. We're told the diagram is not drawn to scale for our answer choices. We have answer choice A H equals 85 K equals 65 answer choice bh equals 65 K equals 45. Answer choice, CH equals 84 K equals 63 and answer choice DH equals 63 K equals 84. All right. So we recall from previous lessons that in order to determine an unknown side, when we have similar triangles, we're going to set up ratios. So we'll have a fraction equal to a fraction. Now, each fraction is going to be its own triangle. So we can call the fraction on the left, that can be the triangle on the left and the fraction on the right, that can be the triangle on the right. The numerators are going to be two sides that are similar to each other. And likewise, the denominators are going to be two sides that are similar to each other. For the numerators, we can choose the two sides that both have one hash mark. And for this first one that we're solving for the denominators, we can choose the two sides that have two hash marks. So from the triangle on the left, the side that has one hash mark that's going in the, in the numerator, that value is 105 that's divided by, from the triangle on the left, the side with two hash marks that is labeled H. So we have 105 divided by H equals. Now, for the triangle on the right, the side that has one hashmark that's labeled that's divided by, from the triangle on the right, the side that has two hash marks that's labeled 20. So 105 divided by H is equal to 25 divided by 20. Now we can use cross multiplication to solve for each. So we'll have 25 multiplied by each. That's 25 H that equals 20 multiplied by 105 20 multiplied by 105 is 2100. So 2000, 100 equals 25 H to solve for H will divide both sides by 25 and we get an H value equal to 84. All right. Now let's work on the final side. So instead of our denominators being the sides with two hash marks, we'll exchange those for the denominators are for the sides that have three hash marks from the triangle. On the left, the side with three hash marks is equal to K. So the K goes in the denominator and for the triangle on the right, the side that has three hash marks is equal to 15, 15 goes in that denominator. So we have 105 divided by K equals 25 divided by 15. Again, we will use cross multiplication now to solve for K. So we have 25 multiplied by K, which is 25 K equals 15, multiplied by 105 15, multiplied by 105 is 1575. That's still equal to 25 K. We'll divide both sides by 25. And on the left, we have K equals and on the right, 1575 divided by 25 is 63. So we have an H value of 84 and A K value of 63. We look at our answer choices and that matches with answer choice. C well done. We'll catch you on the next one.

Find the unknown side lengths in each pair of similar triangles.

Key Concepts

Similar Triangles

Proportionality

Scale Factor

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