Question

area of the triangle whose sides are 18 cm , 24 cm and 30 cm in length. also find the length of the altitude corresponding to the smallest side

any one else will solve this question I will mark it as brainliest..
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Answer 1

$\bigstar \sf \bf \underline{\underline{\red{Given:-}}}$

• sides of a triangle are 18 cm , 24 cm and 30 cm in length.

$\bigstar \sf \bf \underline{\underline{\red{To \ find:-}}}$

• The length of the altitude corresponding to the smallest side.
• Area of the triangle.

$\bf \sf \underline{\underline{ Formulas \ used :-}}$

Heron's formula :

❥ Area of triangle = √s(s-a)(s-b)(s-c)

Where,

=> 's' is the semi perimeter

=> a,b,c are sides .

❥ Area of triangle = 1/2 (base)(height)

$\bigstar \sf \bf \underline{\underline{\red{Solution:-}}}$

Semiperimeter = a+b+c/2

=> S = (18+24+30) / 2

=> s = 36cm.

To find Area of the triangle :-

By heron's formula,

$\implies \sf Area = \sqrt{s(s-a)(s-b)(s-c)} \\\\\\\implies \sf \sqrt{36(36-18)(36-24)(36-30)} \\\\\\\implies \sf \sqrt{46656} = 216 cm^2.$

Hence ,Area of triangle is 216cm².

To find the length of the altitude corresponding to the smallest side :-

$\implies \sf Area = 1/2 (base)(height) \\\\\\\implies \sf 1/2 (18)(height)=216\\\\\\\implies \sf 9(height)= 216 \\\\\\\implies \sf Height = 216/9 = 24cm.$

Hence , The length of the altitude corresponding to the smallest side is 24cm.

________________

HOPE IT HELPS !

Answer 2

$\bigstar \sf \bf \underline{\underline{\red{Given:-}}}$

sides of a triangle are 18 cm , 24 cm and 30 cm in length.

$\bigstar \sf \bf \underline{\underline{\red{To \ find:-}}}$

The length of the altitude corresponding to the smallest side.

Area of the triangle.

$\bf \sf \underline{\underline{ Formulas \ used :-}}$

Heron's formula :

❥ Area of triangle = √s(s-a)(s-b)(s-c)

Where,

=> 's' is the semi perimeter

=> a,b,c are sides .

❥ Area of triangle = 1/2 (base)(height)

$\bigstar \sf \bf \underline{\underline{\red{Solution:-}}}$

Semiperimeter = a+b+c/2

=> S = (18+24+30) / 2

=> s = 36cm.

To find Area of the triangle :-

By heron's formula,

$\implies \sf Area = \sqrt{s(s-a)(s-b)(s-c)} \\\\\\\implies \sf \sqrt{36(36-18)(36-24)(36-30)} \\\\\\\implies \sf \sqrt{46656} = 216 cm^2.$

Hence ,Area of triangle is 216cm².

To find the length of the altitude corresponding to the smallest side :-

$\implies \sf Area = 1/2 (base)(height) \\\\\\\implies \sf 1/2 (18)(height)=216\\\\\\\implies \sf 9(height)= 216 \\\\\\\implies \sf Height = 216/9 = 24cm.$

Hence , The length of the altitude corresponding to the smallest side is 24cm.

________________

HOPE IT HELPS !