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Pythagoras theorem
In a right angled triangle if the length of the perpendicular sides are 5 and 8 then find the length of the third side
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2 Replies
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As per Pythagoras theorem,
the square of length of hypotenuse (3rd or non perpendicular side) = Sum of squares of two perpendicular sides.
Here let us name the two perpendicular sides as a= 5 , b=8 and the 3rd side as c (the hypotenuse)
So using Pythagoras theorem:-
c^2 = a^2 + b^2
=> c^2 = 5^2 + 8^2
=> c^2 = 25 +64
=> c^2 = 89
=> c = √89
=> c = 9.434 (approximate) is the length of 3rd side
(note: students not having access to calculators can stop at the c = √89 step which is also correct )👍
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Pythagoras theorem: Pythagoras theorem states that if there is a right angled triangle having perpendicular sides as length a and length b and length of hypotenuse of the right angled triangle (Hypotenuse is the side opposite to right angle of the triangle) as c then a^2 + b^2 = c^2.
There is also a concept of Pythagorean triplets.
Pythagorean Triplets : Pythagorean triplets are basically the sides of the right angled triangle like a,b,c.
examples: (3,4,5), (6,8,10), (12,16,20) and so on.
This Pythagorean triplets are useful when we have given a question in which two sides are given to us and those two sides are there in the Pythagorean triplet then we can directly write the third side without doing any sort of calculation.
Also if in the question there are given the three sides of the triangle and asked us if it is right angled triangle or not then check the Pythagorean triplets and determine the answer.
In the question it is given that there is a right angled triangle and the length of the first perpendicular side is 5 and second perpendicular side is 8 we have to find the length of the hypotenuse.
we assume that one perpendicular side is of length a and other perpendicular side is of length b and hypotenuse is of length c.
Now we will write what is given in the question.
Given:
a = 5 units
b= 8 units
We have to find the value of length c
The solution is as follows:
According to Pythagoras theorem,
a^2 + b^2 = c^2
therefore, c^2 = 5^2 + 8^2
c^2 = 25 + 64
c^2 = 89 units
c is square root of c^2 that is square root of 89.
c~9.4339 units
Therefore we can say that c is equal to square root of 89 or approximately equal to 9.4339 units
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