Question

Solve by using Pythagorean Theorem, a= 5, b= x-1, and c=x

Answer 1

The value of x is 13, from the values of x the values of a,b and c becomes 5, 12 and 13, which is obtained by using Pythagorean theorem.

Explanation:

The given is,

a = 5

b = x - 1

c = x

Step:1

Pythagorean theorem is,

`a^(2) + b^(2) = c^(2)`................................(1)

( It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides )

From the given values the equation (1) becomes,

`5^(2) + (x-1) ^(2) = x^(2)`

(
`(a-b)^(2) = a^(2) + b^(2) -2ab` )

25 + (
`x^(2)` + 1 - 2x ) =
`x^(2)`

25 + 1 -2x = 0 ( ∵ Eliminate
`x^(2)` in both sides)

26 = 2x

x = 13

Step:2

From the values of x,

a = 5

b = ( 13 - 1 ) = 12

c = 13

Result:

The value of x is 13, from the values of x the values of a,b and c becomes 5, 12 and 13, which is obtained by using Pythagorean theorem.