Algerbra finding the perimeter

Question

I need help with the following question:
the area of a right triangle is 20cm. If the height of the triangle is 4cm then what is the perimeter?

Answer 1

Hi, Hanna,

Q:  What is the perimeter?  Since you were given the area, find the right triangle's area first.

 

P=Base + height + hypotenuse (side opposite 90 degree angle)

 

**Note:  Remember that a right triangle has a 90 degree angle.  The base is what it sits on.

Draw a picture or model of the triangle:

h=4cm  l    

            l           hypotenuse

            l90º___________

                  base

 

A= 20 cm^{2          Area = (1/2) Base (height)}  

 

A= (1/2) B* H

 

 ^{20=(1/2) B(4)         Substitute what you know into the formula.}  

 

20=(4/2) B                       20=2B       Divide both sides by the number next to "B."

 

10=B     Now all you need to find is the length of the hypotenuse in order to  add up all the sides and get the perimeter.  Use the Pythagorean Equation: a²+b²=c²                side² +side²=hypotenuse ²

 

4² + 10²=c²         16+100=c²        116=c²   Take the square root of both sides of the equation.

 

√(116)= c                    You may want to use your calculator here.  Then add up all the sides, and you are done.

 

If I have helped you, please give me a thumbs up.

                                                 Susan C.

 

 

        

 

 

 

 

 

Answer 2

Here's what we know:

A =.5bh (the area is half base times height)

h = 4

A = 20

h² + b² = y² (the squares of the base and height equal the square of the hypotenuse)

 

20 = .5 * 4b

20 = 2b

10 = b

 

4² + 10² = y²

16 + 100 = y2

116 = y²

10.77 ≈ y

 

4 + 10 + 10.77 = 24.77

So the perimeter is about 24.77 cm