The perimeter of an equilateral triangle is 45 meters. find the length of an altitude.

which leads to 

The length of a rectangle is 7 inches more than its width. A diagonal of the rectangle is 13 inches long. What is the length and width of the rectangle?

Clearly this triangle belongs to the 5-12-13 family or right triangles, but if this is not apparent... 

We are given that

substituting into the Pythagorean formula:


 

which can be solved to obtain 

 or  

but since this is geometry we know all measurements are positive,
 ,

this in turn means 

Find the value of x Right triangle with the sides x, 2x+4, 2x+6

sides: x, 2x+4=2(x+2), 2x+6=2(x+3) 
so we write: 

 
 
 

 
 
 
 
which gives us x=-2 or x=10 
but x>0 

so only x=10 works :) 

a right triangle has a leg with length of 5cm and a hypotenuse of 13 cm. find the length of the other leg.

These lengths come from the well known 5-12-13 right triangle. So 12

IF THE DIAGONAL OF RECTANGLE IS 26 FEET AND HEIGHT IS 10 FEET WHAT IS THE BASE?

these numbers put the triangle in the 5-12-13 right triangle family, so the base must be 24

Chris and Pamela leave home at the same time. Chris drives eastward at a rate of 40 miles per hour, while Pamela drives south at 60 miles per hour. Find how far apart they are to the nearest mile after 2 hours.

After 2 hours 
Chris: 80 mi
Pam: 120 mi 
 


:)

The hypotenuse of a 30 – 60-90 right triangle measure 15in. What are the lengths of the longer leg and shorter leg?

We know that a 30-60-90 triangle has certain properties based on one way they are constructed. In particular the shortest side is half the length of the longest and it is root(3) times as long as the shortest side so... 
 in 

 in 



:)

A rectangular pool is 21 meters wide and 28 meters long. If you swim diangonally across the pool, how many meters would you be swimming?

21-28-35 are in the 3-4-5 family of right triangles so 35 meters

a 15 foot ladder leaning against a building touches the wall 12 feet above the ground. How far from the building is the bottom of the ladder

c=15
b=12
a=? 
this triangle is in the 3-4-5 family of right triangles so a=10 ft 

:)

in a right triangle, find the length of the not given. a=8, c=17

Your Answer:

so

a telephone pole breaks and falls as shown. to the nearest foot, what was the original height of the pole? 12ft and 5ft are the sides

Assuming that a=5, b=12 
then this triangle is clearly in the 
 
family of right triangles. And since the broken part has to be the hypotenuse, the original length had to be the shortest side and hypotenuse: 

 
l=18ft