Question

Dana is looking at a nautilus shell and forms similar triangles using different parts of the shell (ANAT ~ ASHL). Dana measures NA = 5 mm, AT = 3 mm, NT = 9 mm, HL = 13 mm. What is SH?

A) 3915 mm
B) 15/13 mm
C) 8/13 mm
D) 65/3 mm

Answer 1

To determine the length of SH in the similar triangles ANAT and ASHL, we set up a proportion based on corresponding sides. After substituting the given measurements and solving the proportion, we find that SH equals 65/3 mm, which matches option D).

Step-by-step explanation:

To find the length of SH in similar triangles ANAT and ASHL when NA = 5 mm, AT = 3 mm, NT = 9 mm, and HL = 13 mm, we can use the properties of similar triangles which state that corresponding sides of similar triangles are proportional. The ratio of corresponding sides in two similar triangles is equal. Therefore, we can form the following proportion:

NA/NT = SH/HL

Substituting in the given values:

5/9 = SH/13

Now we solve for SH by cross-multiplying:

5 × 13 = 9 × SH

65 = 9 × SH

We then divide both sides by 9:

SH = 65/9

SH = 65/3 mm

Thus, the length of SH is 65/3 mm which corresponds to option D).