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
.
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, and 24 inches; All of the side lengths of the smaller triangles have been multiplied by 2, which guarantees side-side-side similarity.

Side 1:   8 inches * 2 = 16 inches
Side 2: 10 inches * 2 = 20 inches
Side 3: 12 inches * 2 = 24 inches.