Question

the sides of triangle are 8 cm,4 cm and 8 cm.the length of the longest altitude is?A) 16root5 cm B)10root5 cm C)2root15 cm D)None of these​

Answer 1

Answer:

triangle is have 4 cornes this is your answer

Answer 2

★Given:-

• Sides of triangle are 8 cm,4 cm and 8 cm.

★To find:-

• Length of longest altitude.

★Solution:-

Using the formula,

$\displaystyle \leadsto \underline{\boxed{\sf Area\ of\ \triangle = \sqrt{s(s-a)(s-b)(s-c)}}}$

Where,

• a,b,c are sides of triangle
• s = semi-perimeter

$\displaystyle \leadsto \underline{\boxed{\sf s = \frac{a+b+c}{2} }}$

Putting values,

➜s = (a+b+c)/2

➜s = (8+4+8)/2

➜s = 20/2

➜s = 10cm

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

$\implies \sf \sqrt{10(10-8)(10-4)(10-8)}$

$\implies \sf \sqrt{10(2)(6)(2)} \\\\\implies \sf Area = 4\sqrt{15} cm^2.$

Using the formula,

$\leadsto \underline{\boxed{\sf Area\ of\ \triangle = \frac{1}{2}\times base\times height }}$

As the area of the triangle is fixed,for the longest altitude we need smallest base.So, the length of base = 4cm.

Putting values,

$\implies \sf Area = \frac{1}{2} bh$

$\implies \sf 4\sqrt{15} = \cfrac{1}{2} \times 4\times h \\\\\implies \underline{\boxed{\sf h = 2\sqrt{15} }}$

Therefore,

The length of longest altitude is 2√15cm.

Option(C) is correct.

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