SSC CHSL 2024 PYQ — Question 58

The correct answer is Option 1 i.e. $16\sqrt5$.

The sides of the triangle are MN = 36 cm, MT = 36 cm, NT = 48 cm

Now,

Semi perimeter(s) = (MN + MT + NT)/2

⇒ s = (36 + 36 + 48)/2

⇒ s = 120/2 = 60 cm

Now,

Area of the triangle = $\sqrt{s(s-MN)(s-MT)(s-NT)}$

⇒ $\sqrt{60(60-36)(60-36)(60-48)}$

⇒ $\sqrt{60\times 24 \times 24 \times 12}$ = 288$\sqrt5$

Now,

Area of the triangle = 1/2 × base × height(h)

⇒  288$\sqrt5$ = 1/2 × 36 × h

⇒  288$\sqrt5$ = 18 × h

⇒ h = 16$\sqrt5$ cm

Thus, The altitude of side MT is approximately 16$\sqrt5$ cm