The two sides of the triangle are 30 and 40 cm. The length of the median drawn to the third side

| September 3, 2021 | education

The two sides of the triangle are 30 and 40 cm. The length of the median drawn to the third side is 25 cm. Find the area of the triangle?

Let a triangle ABC be given, we supplement its sides so that we get a parallelogram ABCD, where BK is the median.
Then, AD = BC, AB = CD.
The ABC area is equal to half of the ABCD area.
At the same time, the area ABCD is the sum of the two areas of the triangle ABD.
So Sabc = Sabd.
Therefore, to begin with, we find the area ABD (since all sides of ABD are known), which we calculate using Heron’s formula.
BD = 2 * BK = 50 cm.
AB = 30 cm.
BC = 40 cm.
Sabd = (p * (p – BD) * (p – AB) * (p – BC)) ^ (1/2),
p = (BD + AB + BC) / 2 = (50 + 30 + 40) / 2 = 60.
Sabd = (60 * (60 – 50) * (60 – 30) * (60 – 40)) ^ (1/2) = (60 * 10 * 30 * 20) ^ (1/2) = 600 (cm ^ 2).
Thus, Sabd = Sabc = 600 (cm ^ 2).



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