In each figure, there are two similar triangles. Find the unknown...

Question

In each figure, there are two similar triangles. Find the unknown measurement. Give any approximation to the nearest tenth.

Accepted Answer

Welcome back. I am so glad you're here. We're told for the following diagram of similar triangles determine the value of B. We are given a diagram with two similar triangles. They're Isosceles triangles and one is inscribed within the other one. They share the same angle that is opposite of both of their bases. The base for the larger Isosceles triangle is labeled B and then the leg for the larger Isosceles triangle is broken into two parts. Part of it is labeled 15. That's the part that is not attached to the smaller inscribed triangle. And the part of the larger triangle's leg that is attached to the smaller triangle is labeled five. So for the smaller triangle, its leg is equal to five and its base is equal to 13. We're told that this diagram is not drawn to scale. For our answer choices, we have answer choice A B equals 52. Answer choice BB equals 39 answer choice CB equals 47 and answer choice DB equals 34. All right. So to solve for an unknown side of a triangle, when we have similar triangles, we can set up a ratio. So we'll have a fraction equal to another fraction. Each fraction is going to be its own triangle. So we can say the fraction on the left is going to be the larger triangle and the fraction on the right is going to be the smaller triangle. And the numerators are going to have to be two similar sides. And the denominators are going to have to be the two similar sides. So we can say for our numerators, those can be the bases. And for the denominators, those can be the legs. So for the larger triangle, its base is B, we don't know that one. For the larger triangle, its leg, that's going to be this whole thing five plus 15. So we can put five plus 15. For now, for the smaller triangle, its base is 13 and for the smaller triangle, its leg is five. Now, it's just a matter of simplifying and solving for B. So on the left hand side in the denominator five plus 15 is 20. So we can rewrite this B divided by 20 equals 13, divided by five. Now, we can use cross multiplication to solve for B and so we'll have five, multiplied by B is five B equals, we can put 20 multiplied by 13. For now, before getting that big number, we can divide both sides by five to solve. For B. On the left hand side, we've got B by itself now. And on the right, we can take the 20 multiplied by 13, divide it by five and simplify the 20 the five, so that 20 becomes a four and four multiplied by equals 52. And so that's how we get our solution for B we look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

In each figure, there are two similar triangles. Find the unknown measurement. Give any approximation to the nearest tenth.

Key Concepts

Similar Triangles

Proportionality in Triangles

Using Ratios to Solve for Unknowns

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