Question

elena is building a garden in the shape of a right triangle. the legs are 6 ft and 8 ft long. she wants to find the diagonal path that cuts across the triangle.
question 1
which formula should elena use to find the diagonal of her right triangle?
$a^{2}+b^{2}=c^{2}$
$c^{2}=ab$
$a + b = c$
$a^{2}-b^{2}=c^{2}$
question 2
what is the length of the diagonal?
14 ft

Explanation:

Step1: Identify the formula for a right - triangle

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) is used.

Step2: Substitute the values of \(a\) and \(b\)

Given \(a = 6\) and \(b = 8\), we substitute into the formula: \(6^{2}+8^{2}=c^{2}\).
So, \(36 + 64=c^{2}\).

Step3: Calculate \(c^{2}\)

\(36+64 = 100\), so \(c^{2}=100\).

Step4: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{100}\).
Since \(c>0\) (length), \(c = 10\).

Answer:

1. The formula \(a^{2}+b^{2}=c^{2}\) should be used.
2. The length of the diagonal is \(10\) ft.