In △LMN, medians MX and NY are perpendicular to each other and intersect at Z. If MX = 20 cm and NY = 30 cm, what is the area of △LMN (in cm²)?

Correct option is B

Given:

Medians MX = 20 cm

Median NY = 30 cm

Medians are perpendicular

Concept Used:
The area of a triangle using two medians $$m_1$$​ and $$m_2$$​ perpendicular to each other is given by:

Area = $$\frac{4}{3} \times \text{Area of parallelogram formed by medians}$$​​

​$$= \frac{4}{3} \times \frac{1}{2} \times m_1 \times m_2$$​​

Solution: 

Using the property;

Area of triangle = $$= \frac{4}{3} \times \frac{1}{2} \times 20 \times 30$$​​

$$=\frac{2}{3} \times 20 \times 30$$​​

​$$= \frac{2}{3} \times 600 = 400 \text{ cm}^2$$​​

Thus, Area of △LMN = 400 cm²