FIND THE MISSING SIDE OF A RIGHT TRIANGLE

The square of hypotenuse is equal to sum of squares of other two sides.

c2 = a2 + b2

Find the values of the unknowns in the following triangles :

Problem 1 :

Solution :

Using Pythagorean theorem.

x2 = 62 + 82

x2 = 36 + 64

x2 = 100

x = 10

So, the unknown value is 10.

Problem 2 :

Solution :

(25)2 = (15)2 + x2

625 = 225 + x2

625 – 225 = x2

400 = x2

20 = x

So, the unknown value is 20.

Problem 3 :

Solution :

(30)2 = (18)2 + x2

900 = 324 + x2

900 – 324 = x2

576 = x2

24 = x

So, the unknown value is 24.

Problem 4 :

Solution :

x2 = 22 + (1.5)2

x2 = 4 + 2.25

x2 = 6.25

x = 2.5

So, the unknown value is 2.5.

Problem 5 :

Solution :

x2 = 22 + 22

x2 = 4 + 4

x2 = 8

x = 2.828

So, the unknown value is 2.828.

Problem 6 :

Solution :

x2 = 32 + 32

x2 = 9 + 9

x2 = 81

x = 9

So, the unknown value is 9`.

Problem 7 :

Solution :

By observing the figure.

Using Pythagorean theorem.

x2 = (10)2 + (10)2

x2 = 100 + 100

x2 = 200

x = 14.14

So, the unknown value is 14.14.

Problem 8 :

Solution :

x2 = (√2)2 + (√2)2

x2 = 2 + 2

x2 = 4

x = 2

So, the unknown value is 2.

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