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

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Answer 1 · 2018-04-25T15:57:20

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

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#