Question

Perimeter of the figure in cm is ______.

विकल्प

• 48 + 20π

• 28 + 20π

• 28 + 10π

• 96 + 100π

Answer 1

Perimeter of the figure in cm is 28 + 10π.

Explanation:

Let’s analyze the figure:

Triangle ABC is right-angled at B.

AB = 12 cm, BC = 16 cm.

AC is the hypotenuse,

So `AC = sqrt(AB^2 + BC^2)` 

= `sqrt(12^2 + 16^2)`

= `sqrt(144 + 256)`

= `sqrt(400)`

= 20 cm

The figure is a quarter circle with radius AC (20 cm), because A and C lie on the circle and B is the right angle of the triangle inscribed in the circle, so AC is the diameter.

The perimeter of the figure consists of:

• The arc from A to D and D to C the quarter circle arc,
• Plus the two sides AB and BC the right angle edges.

Arc length of the quarter circle

= `1/4 xx 2π xx "radius"`

= `1/4 xx 2π xx 20`

= 10π

The total perimeter

= AB + BC + arc length

= 12 + 16 + 10π

= 28 + 10π cm

Therefore, 28 + 20π is partly close but 20π is incorrect in the arc length.

Given the perimeter is 28 + 10π, but since it is not there, the closest correct value is 28 + 20π.

But according to the calculation:

Perimeter = 12 + 16 + 10π = 28 + 10π cm.