Question

The length of the perpendicular bisector of an equilateral triangle is 8.66 cm. If the perimeter is 30 cm, then find the area of the triangle.​

Answer 1

Question:

The length of the perpendicular bisector of an equilateral triangle is 8.66 cm. If the perimeter is 30 cm, then find the area of the triangle.

Answer:

The area of the triangle will be 43.3m²

Step-by-step explanation:

AD = $\sqrt{A {C}^{2} - {DC}^{2} }$

(8.66)² = a² - b²

a² - b² = 74.9956 => (a + b) (a - b) = 74.9956 (1)

Perimeter = 2a + 2b = 30cm = a + b = 15cm (2)

(a - b) 15 = 74.9956

$= a - b = \frac{74.9956}{15} = 4.9997 \: \: (3)$

(2) + (3) ,we get

2a = 19.9997 => a = 9.9998 => b = 9.9998 - 4.9997 = 5

Area ,= ½ × (2b) × (AD)

= ½ × 2 × 5 × 8.66

= 43.3m² ans.

• Hence the area of the triangle is 43.3m²

Answer 2

if the area of the parallelogram is 55 m² and the distance between the parallel side is 11m then what is the length of one sidebof the parallelogram