Question

What are the lengths?

Answer 1

In both the figures we have a Right Angled Triangle.

Two sides of the right angled triangles are given and we are to find the Third side. This can be done using the Pythagoras Theorem, which states:

Hypotenuse² = Base² + Perpendicular²

For 1st figure, we have
Base = 21
Perpendicular = 20

So, 

Hypotenuse² = 20² + 21² = 841
⇒
Hypotenuse = 29 (1st option is correct)

For 2nd Image, we have
Base= 6
Hypotenuse = 10

So, we can write:

10² = 6² + Perpendicular²
Perpendicular² = 64
⇒
Perpendicular = 8 (Option Fourth)