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Find $X$ and the given problem is $x^2 = 7^2 + 24^2$

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Composition of linear and quadratic functions: find a value

Full solution

Q. Find

X

and the given problem is

x^2 = 7^2 + 24^2

Understand the problem: Understand the problem. $\newline$ We need to find the value of $X$ such that $X^2 = 7^2 + 24^2$ . This is a direct application of the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse ( $X$ ) is equal to the sum of the squares of the lengths of the other two sides ( $7$ and $24$ in this case).
Calculate squares of numbers: Calculate the squares of $7$ and $24$ . $\newline$ $7^2 = 49$ $\newline$ $24^2 = 576$ $\newline$ Now, add these two values to find the sum of the squares. $\newline$ $49 + 576 = 625$
Set up equation for $X^2$ : Set up the equation for $X^2$ . $X^2 = 7^2 + 24^2$ $X^2 = 625$
Solve for X: Solve for X. $\newline$ To find X, we take the square root of both sides of the equation. $\newline$ $X = \sqrt{625}$ $\newline$ $X = 25$

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