Question

I’m confused on this one

Answer 1

You first need to find the length of the line bisecting the triangle. You can find this using the Pythagorean Theorem.

Pythagorean Theorem: a² + b² = c²
a and b are the legs; c is the hypotenuse

Let's focus on the left triangle. You know that its hypotenuse is 17 cm, and that its base is 4 cm (because the tic on the line is showing you that it is congruent to the other triangle's base).

Plug in 4 for a, 17 for c, and solve for b to find the side we need first (the triangle bisector).

4² + b² = 17²
Rewrite this with 4 and 17 squared.

16 + b² = 289
Subtract 16 from both sides.

b² = 273
Square root both sides to isolate b.

b = √273 = 16.5 cm (rounded to tenths)
The triangle bisector length is 16.5 cm.

Now to find the hypotenuse of the triangle on the right (the "missing length" that you're supposed to find), plug in 4 for a, 16.5 for b, and solve for c.

4² + 16.5² = c²
Square 4 and 16.5; rewrite.

16 + 272.25 = c²
Add 16 and 272.25.

288.25 = c²
Square root both sides to isolate c.

c = √288.25 =17 cm 
The missing length is 17 cm.