Question

question 3
10 pts
g.gsr.6.1 (mc)
find the value of x.
image of a right triangle with legs 7 and 7, hypotenuse x
options:
x = √2
x = 7
x =14
x = 7√2

Explanation:

Step1: Identify Triangle Type

The triangle is right - angled with two legs of length 7. So, it is an isosceles right - triangle.

Step2: Apply Pythagorean Theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\). Here, \(a = 7\), \(b = 7\), and \(c=x\).
Substitute the values into the formula: \(x^{2}=7^{2}+7^{2}\)
\(x^{2}=49 + 49=98\)

Step3: Solve for x

Take the square root of both sides: \(x=\sqrt{98}\)
Simplify \(\sqrt{98}\): \(\sqrt{98}=\sqrt{49\times2}=\sqrt{49}\times\sqrt{2}=7\sqrt{2}\)

Answer:

\(x = 7\sqrt{2}\) (the option with \(x = 7\sqrt{2}\))