If a right triangle has a hypotenuse of 6, and a perimeter of 14, what is the area of the right triangle?

1 Answer
Apr 25, 2018

color(blue)(6 \ \ \ \"units"^2)

Explanation:

By Pythagoras' theorem, the square on the hypotenuse is equal to the sum of the squares of the other two sides.

Let the two unknown sides be bba and bb(b)

Then:

a^2+b^2=36 \ \ \ \ [1]

The perimeter of a triangle is the sum of all its sides.

a+b+6=14 \ \ \ \ [2]

Using [2]

a=6-b

Substituting in [1]

(6-b)^2+b^2=36

Expanding:

b^2-12b+36+b^2=36

2b^2-12b=0

Factor:

2b(b-6)=0=>b=0 and b=6

b=0 is not valid, we can't have a triangle with no side.

Substituting b=6 in [2]

a+6+6=14

a=2

Area of triangle is:

1/2"base"xx"height"

1/2(6)*(2)=6 \ \ \ \"units^2