The square of hypotenuse is equal to sum of squares of other two sides.
c^{2} = a^{2} + b^{2}
Find the values of the unknowns in the following triangles :
Problem 1 :
Solution :
Using
Pythagorean theorem.
x^{2} = 6^{2} + 8^{2}
x^{2} = 36 + 64
x^{2} = 100
x = 10
So, the unknown value is 10.
Problem 2 :
Solution :
(25)^{2} = (15)^{2} + x^{2}
625 = 225 + x^{2}
625 – 225 = x^{2}
400 = x^{2}
20 = x
So, the unknown value is 20.
Problem 3 :
Solution :
(30)^{2} = (18)^{2} + x^{2}
900 = 324 + x^{2}
900 – 324 = x^{2}
576 = x^{2}
24 = x
So, the unknown value is 24.
Problem 4 :
Solution :
x^{2} = 2^{2} + (1.5)^{2}
x^{2} = 4 + 2.25
x^{2} = 6.25
x = 2.5
So, the unknown value is 2.5.
Problem 5 :
Solution :
x^{2} = 2^{2} + 2^{2}
x^{2} = 4 + 4
x^{2} = 8
x = 2.828
So, the unknown value is 2.828.
Problem 6 :
Solution :
x^{2} = 3^{2} + 3^{2}
x^{2} = 9 + 9
x^{2} = 81
x = 9
So, the unknown value is 9`.
Problem 7 :
Solution :
By observing the figure.
Using Pythagorean theorem.
x^{2} = (10)^{2} + (10)^{2}
x^{2} = 100 + 100
x^{2} = 200
x = 14.14
So, the unknown value is 14.14.
Problem 8 :
Solution :
x^{2} = (√2)^{2} + (√2)^{2}
x^{2} = 2 + 2
x^{2} = 4
x = 2
So, the unknown value is 2.
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