Question

a right triangle has legs with lengths of 11 centimeters and 9 centimeters. what is the length of this triangles hypotenuse, in centimeters?
a) $sqrt{40}$
b) $sqrt{202}$
c) 20
d) 202
question 13
what is the diameter of the circle in the xy - plane with equation $(x - 5)^2+(y - 3)^2 = 16$
a) 4
b) 8
c) 16
d) 32

Explanation:

Question 12

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 11\) and \(b = 9\).
So \(c^{2}=11^{2}+9^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(11^{2}=121\) and \(9^{2}=81\), then \(c^{2}=121 + 81=202\).

Step3: Find \(c\)

\(c=\sqrt{202}\)

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^{2}+(y - k)^{2}=r^{2}\), where \((h,k)\) is the center of the circle and \(r\) is the radius. Given \((x - 5)^{2}+(y - 3)^{2}=16\), we have \(r^{2}=16\), so \(r = 4\).

Step2: Calculate the diameter \(d\)

The diameter \(d\) of a circle is related to the radius \(r\) by \(d = 2r\). Since \(r = 4\), then \(d=2\times4 = 8\).

Answer:

B. \(\sqrt{202}\)

Question 13