Question

Use the given figure to find the length of x.

Answer 1

x = 18

Explanation:

This problem can be solved using concept of Pythagoras theorem.

Pythagoras theorem states that in a right angled triangle, if "a" and "b" are sides containing the right angle and h is hypotenuse then the relation between them is
`a^2 + b^2 = h^2`

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Given in the problem

a = 24

b = x

h = x+12

applying Pythagoras theorem

`24^2 + x^2 = (x+12)^2\\=> 576 + x^2 = x^2 + 24x + 144\\=>576 = x^2 + 24x + 144 - x^2\\=> 576 = 24x + 144 \\=> 576 - 144= 24x\\=> 432 = 24x\\=> x = 432/24 = 18`

for (x+12)^2 we have used formula
`(a+b)^2 = a^2 + 2ab + b^2`

Thus, value of x is 18.