Question

Xenia is designing a large sail, in the shape of an isosceles triangle, for a model sailboat. The length of the median to the base side is 63 mm. The midsegment parallel to the base is 16mm long. What is the length of the slant sides of the sail?

A. 31.5 mm
B. 47.5 mm
C. 79 mm
D. 127 mm

Answer 1

The length of the slant sides of the sail is approximately 32.5 mm.

Step-by-step explanation:

Let's start by understanding the given information. The sail is in the shape of an isosceles triangle, which means that two sides are equal in length. The length of the median to the base side is 63 mm, which is the same as the length of the midsegment parallel to the base.

In an isosceles triangle, the median to the base is also the altitude. Therefore, the length of the slant sides can be found by using the Pythagorean theorem. Let x be the length of each of the equal sides.

Using the Pythagorean theorem, we have:

x^2 = (63/2)^2 + 16^2

x^2 = 3969/4 + 256

x^2 = 4225/4

x = √(4225/4)

x = √1056.25

x ≈ 32.5 mm

Therefore, the length of the slant sides of the sail is approximately 32.5 mm.