Question

14)
the drawing shows the measurements
in a section of a circular design. how
long is the radius of the circle?
f 10 cm
g 8.7 cm
h 7 cm
j 4.3 cm
15)
in the figure, what is the value of x?
f 6
g 6\sqrt{2}
h 6\sqrt{3}
j 12

Explanation:

Step1: Identify the triangle type

The triangle is a right - angled isosceles triangle (since one angle is \(90^{\circ}\) and another is \(45^{\circ}\), so the third angle is also \(45^{\circ}\)). For a right - angled isosceles triangle with legs of length \(a\) and hypotenuse \(x\), the relationship is \(x = a\sqrt{2}\) (derived from the Pythagorean theorem \(x^{2}=a^{2}+a^{2}=2a^{2}\)).

Step2: Substitute the value of the leg

Here \(a = 6\). Substituting into the formula \(x=a\sqrt{2}\), we get \(x = 6\sqrt{2}\).

Answer:

G. \(6\sqrt{2}\)