Question

The sides of a triangle are 35cm, 54cm and 61cm respectively: The length of its longest altitude is ​

Answer 1

Answer:

ɪꜱ 64 ᴄᴍ

Step-by-step explanation:

ʜᴏᴩᴇ ɪᴛʜᴇʟᴩꜱ ᴜ !!!!!!!!

Answer 2

Answer:-

$\sf \: a = 35, b = 54, c = 61$

$\sf \: s = \frac{(a + b + c)}{2}$

$\sf \longrightarrow \: s = \frac{(35 + 54 + 61)}{2}$

$\sf \longrightarrow \frac{150}{2}$

$\sf \longrightarrow75$

$\sf$

$\sf \: Area(Δ) = \sqrt{s(s-a)(s-b)(s-c) }$

$\sf \: ⇒ Area(Δ) = \sqrt{75(75-35)(75-54)(75-61) }$

$\sf \: ⇒ Area(Δ) = \sqrt{75×40×21×14 }$

$\sf \: ⇒ Area(Δ) = 420 \sqrt{5} \: cm^{2}$

$\sf$

$\sf \: Area(Δ) = \frac{1}{2} × Base × Altitude$

★ As the area of the triangle is fixed, for the longest altitude we need smallest base.

So, the length of base = 35cm

$\sf \: Area(Δ) = \frac{1}{2} × Base × Altitude$

$\sf \: ⇒ 420 \sqrt{5} = \frac{1}{2} × 35 × Altitude$

$\sf \: ⇒ 24 \sqrt{5} = Altitude.$

$\sf$

Hence, the correct option is (C).