Question

Find the value of x.

Answer 1

Pythagorean Theorem:

`\quad\quad\quad \boxed{ \tt{\color{blue}{c}^(2) = {a}^(2) + {b}^(2) }}`

To find the value of x. Let's use this formula:

`\quad\quad\quad \boxed{ \tt{\color{blue}{a} = \sqrt{ {c}^(2) - {b}^(2) \: \: } }}`

Imagine that "a" is the "x".

`\quad\quad\quad \boxed{ \tt{\color{black}{a} = \sqrt{ {c}^(2) - {b}^(2) \: \: } }}`

`\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {c}^(2) - {b}^(2) \: \: } }}`

`\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {7}^(2) - {4}^(2) \: \: } }}`

`\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {49} - {16} \: \: } }}`

`\quad\quad\quad \boxed{ \tt \color{black}{{x} = √( 33) }}`

Hence, The value of x is,

`\quad\quad\quad \boxed{ \tt \color{green}{{x} = √( 33) }}`

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Answer 2

x = sqrt(33)

Explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

4^2 + x^2 = 7^2

16 + x^2 = 49

Subtract 16 from each side

x^2 = 49-16

x^2 = 33

Take the square root of each side

sqrt(x^2) = sqrt(33)

x = sqrt(33)