Please Help!
One leg of a right triangle measures 4 units, and the hypotenuse measures x units.



If the area of the triangle, A, is a function of x, which equation is a correct representation of A?

Please Help One leg of a right triangle measures 4 units and the hypotenuse measures x units If the area of the triangle A is a function of x which equation is class=

Respuesta :

msm555

Answer:

C) [tex] A(x) = 2 \sqrt{x^2 - 16} [/tex]

Step-by-step explanation:

The area [tex] A [/tex] of a right triangle can be calculated using the formula:

[tex] \Large\boxed{\boxed{ A = \dfrac{1}{2} \times \textsf{base} \times \textsf{height}}} [/tex]

In this case, one leg of the right triangle measures 4 units, and the hypotenuse measures [tex] x [/tex] units.

Let's denote the other leg of the triangle as [tex] y [/tex] units.

Using the Pythagorean theorem, we have:

[tex]c^2 = a^2 + b^2[/tex]

[tex] x^2 = 4^2 + y^2 [/tex]

[tex] x^2 = 16 + y^2 [/tex]

[tex] y^2 = x^2 - 16 [/tex]

[tex] y = \sqrt{x^2 - 16} [/tex]

Now, the area [tex] A [/tex] of the triangle can be expressed as:

[tex] A(x) = \dfrac{1}{2} \times 4 \times \sqrt{x^2 - 16} [/tex]

[tex] A(x) = 2 \sqrt{x^2 - 16} [/tex]

Therefore, the correct representation of [tex] A(x) [/tex] is:

[tex] A(x) = 2 \sqrt{x^2 - 16} [/tex]