Question 107382: find the perimeter of right triangle ABC if the legs are 3 inches and 4 incehs. Found 2 solutions by solver91311, TP:Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website! There are two ways to go after this one. The simple way is to recall that a right triangle with legs of 3 and 4 has a hypotenuse that measures 5. (3-4-5 right triangle). 3+4+5 = 12.
Or, if you don't recall the 3-4-5 right triangle, you can fall back on our good friend Pythagoras who said that the square on the hypotenuse is equal to the sum of the squares on the other two sides, or symbolically:
, or in terms of c (the value we need to determine),
In this case: .
Again, our sides are 3, 4, and 5, so our perimeter must be 12.
You can put this solution on YOUR website! You need to know that in a right angled triangle the sum of the squares of the "legs" is equal to the square of the longest side(the hypotenuse).
This is known as Pythagoras's Theorem and apparently it was used in the building of the Pyramids!
In order to find the perimeter(the distance all round) of the triangle we need to know the length of the third side and since it is a right angled triangle we can use this theorem.
Using algebra the theorem states: a^2+b^2=c^2 where a and b are the "legs" and c is the hypotenuse.
In your question a=3ins and b=4ins and so 3^2+4^2=c^2.
Hence c^2= 9+16=25.
So c==5 (strictly speaking = plus or minus 5 but in the context of the question c must =5,since it is a length(a scalar quantity)). So the sides are 3,4 and 5 inches.
Hence the perimeter is 3+4+5=12 inches ANS
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