# How do you find the perimeter of a right triangle with the area 9 inches squared?

##### 2 Answers

#### Answer:

37, 20.2, or 15.7 inches.

#### Explanation:

Area of a triangle (A) =

Perimeter (P) = all sides added up.

Right triangle: right angled triangle?

So from pythagoras,

We've been given A:

So

As we haven't been given any other conditions, except that it's a right angled triangle, there will be multiple correct answers.

As

Any of these can be right angled triangles, as we haven't been given any parameters for the hypotenuse.

We can still find the perimeters for these different dimensions of the triangle, using pythagoras.

If b=1, h=18, then hypotenuse =

If b=2, h=9, hypotenuse =

If b=3, h=6, hypotenuse =

#### Answer:

The minimum possible perimeter occurs when the triangle has sides:

#3sqrt(2)# ,#3sqrt(2)# and#6# ,

giving a perimeter of

#### Explanation:

A right triangle of area

If one side of the rectangle is of length

By Pythagoras, the length of the diagonal is:

#sqrt(t^2+(18/t)^2)#

and the perimeter of the right triangle is:

#t + 18/t + sqrt(t^2+(18/t)^2)#

Notice that if

The minimum possible value of the perimeter occurs when

That is, when:

#t = sqrt(18) = 3sqrt(2)#

Then the perimeter is:

#3sqrt(2) + 3sqrt(2) + sqrt(18+18) = 6+6sqrt(2)#