Solve problems on radicals

Question

Write the given , draw a figure then show the solution . 

1. ) A cube has a surface area of 72 mm Find the length of an edge of the cube.

2. A kite is secured to a rope that is tied to the ground . A breeze blows the kite so that the rope is taugh while the kite is directly above a flagpole that is 40ft from where the rope is staked down . Find the altitude of the kite if the rope is 100 ft long.

Answer 1

surface area of a cube = 72 = 6s^2 where s^2 = area of a side, s=edge length

s^2 = 72/6 = 12 mm = edge length length

the 100 foot rope is the hypotenuse of a right triangle with base = 40 feet

use the Pythagorean Theorem.

and height squared = 100^2 - 40^2

= 10,000 - 1600

= 8400

height =sqr8400 = slightly less than 290 feet