Question

X
3.
What is the value of x to the nearest tenth?
6
24

Answer 1

Answer:

• C. 13.4

=======================

Connect the center with one end of the chord, this gives us a right triangle with hypotenuse of x, one leg of 6 and another leg of 24/2 = 12.

Use Pythagorean to find the value of x:

• x² = 6² + 12²
• x² = 36 + 144
• x² = 180
• x = √180
• x = 13.4 (rounded)

Correct choice is C.

Answer 2

Answer:

x = 13.4

Step-by-step explanation:

Definitions

Radius: a straight line from the center of the circle to its circumference.

Chord: a straight line joining two points on the circle.

Perpendicular:  at a right angle (90°).

Isosceles triangle: a triangle with 2 sides of equal length and 2 congruent base angles.

From inspection of the given diagram:

• radius = x
• chord = 24 units
• segment of the radius perpendicular to the chord = 6 units

If lines are drawn from the center of the circle to the endpoints of the chord, an isosceles triangle is created with base of 24 units and height of 6 units.  

The isosceles triangle is made up of two right triangles with base of 12 units and height of 6 units.  The radii are the hypotenuse of these right triangles.  Therefore, to calculate the radius of the circle (x), use Pythagoras Theorem.

Pythagoras Theorem

$\sf a^2+b^2=c^2$

where:

• a and b are the legs of the right triangle
• c is the hypotenuse (longest side) of the right triangle

Therefore:

$\sf \implies 6^2+12^2=x^2$

$\implies \sf x^2=36+144$

$\implies \sf x^2=180$

$\implies \sf \sqrt{x^2}=\sqrt{180}$

$\implies \sf x=\pm 6\sqrt{5}$

As length is positive:

$\implies \sf x = 6\sqrt{5}=13.4\:units\:(nearest\:tenth)$

Learn more about Pythagoras Theorem here:

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