Question

19. The perimeter of an equilateral triangle is 30 cm. Then its area is
(a) 25 cm?
(b) 25v5 cm (c) 2513 cm
(d) 60 cm​

Answer 1

A≈43.3cm²
P Perimeter

cm
Unit Conversion:
P=30cm
Using the formulas
A=3
4a2
P=3a
Solving forA
A=3P2
36=3·302
36≈43.30127cm²

Answer 2

Answer:

Option (b)

Step-by-step explanation:

An equilateral triangle, as the name specifies, has equal angles and equal sides.

A triangle has three sides, and the perimeter is the sum of all three sides.

Let us take the side as x.  Using the property above, x + x + x = 30.

3x = 30.

x = 10 cm.

Now, let us draw a median from A to a point R such that it bisects BC and is perpendicular to BC.

⇒ ∠ARC = ∠ARB = 90°.

Now, we can find the length of the median using the Pythagoras theorem.

$AR^2 + RC^2 = AC^2$

$x^2 + 5^2 = 10^2$

$x^2 = 75$

$x = 5\sqrt{3}$

x cannot be negative, as it is a side length.

Now, we can find the area, by multiplying the base and height and dividing the product by 2.

$A = bh/2$

$A = 10(5\sqrt{3})/2$

$A = 25\sqrt{3}$ cm.

Option (b)