Question

Bryan purchased two triangular wall shelves. The sides of each shelf are 8 inches, 10 inches, and 12 inches. He's trying to build a similar, larger triangular shelf to hang between the smaller ones. Which of the dimensions can Bryan use for the larger shelf so that it is similar to the ones he purchased? Justify why the three triangles are similar.

A) 4 inches, 5 inches, and 6 inches; All of the side lengths of the smaller triangles have been multiplied by 1/2 which guarantees side-side-side similarity
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B) 16 inches, 20 inches, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees side-side-side similarity.
C) 16 inches, 20 inches, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees side-angle-side similarity.
D) 16 inches, 20 inches, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees angle-angle-side similarity.

Answer 1

(B) 16 inches, 20 inches, 24 inches; All the side lengths of the smaller triangles have been multiplied by 2, which guarantees side-side-side similarity.

Explanation:

The sides of the triangular wall shelves are given as 8 inches, 10 inches and 12 inches. In order to build a larger, similar triangle he must multiply the sides of the triangle wall by 2 so that it follows the similarity conditions,that is:

`(16)/(8) =(20)/(10)=(24)/(12) =(2)/(1)`

Since, we were given the sides of the triangular wall shelves, therefore the new triangle formed will also be formed of three sides.

Hence, Option (B) is correct in which all the sides of smaller triangles are multiplied by 2 which guarantees side-side-side similarity.

Answer 2

The correct answer is letter B) 16 inches, 20 inches, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees side-side-side similarity. Similar angles shows congruence when their sides are proportional.