Question

Find the area of a triangle whose medians are 18 24 30

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The area of a triangle whose medians are 18, 24, and 30 is 288.

Step-by-step explanation:

We have to find the area of a triangle whose medians are 18, 24, and 30.

Firstly, as we know that the area of a triangle with the medians given has the following formula;

 Area of a triangle =  $\frac{4}{3} \times \sqrt{s(s-a)(s-b)(s-c)}$

where,  $s = \frac{\text{Sum of all the three medians}}{2}$

So,  $s = \frac{a+b+c}{2}$  ⇒  $s = \frac{18+24+30}{2}$

                               =  $\frac{72}{2}$  = 36

Now, substituting the value of s in the area formula, we get;

        Area of a triangle =  $\frac{4}{3} \times \sqrt{s(s-a)(s-b)(s-c)}$  

                                      =  $\frac{4}{3} \times \sqrt{36(36-18)(36-24)(36-30)}$

                                      =  $\frac{4}{3} \times \sqrt{36\times 18 \times 12 \times 6}$

                                      =  $\frac{4}{3} \times 216$

                                      =  $4 \times 72$ = 288

Hence, the area of a triangle whose medians are 18, 24, 30 is 288.