Question

The area of triangle with given two sides
18cm and 10cm respectively and perime
equal to 42 cm is: *​

Answer 1

Answer :

Given :

• Sides = 18 cm and 10 cm

• Perimeter = 42 cm

To Find :

• Area of triangle

Solution :

• Perimeter of ∆ = Sum of all the sides

➡ Let the third side be x

$\leadsto \sf 42\:=\:18\:+\:10\:+\:x$

$\leadsto \sf 42\:=\:28\:+\:x$

$\leadsto \sf x\:=\:42\:-\:28$

$\leadsto \sf x\:=\:14$

Now , we will find area by heron's formula .

• Here , a = 18 , b = 10 and c = 14

↪Also , semi perimeter = 42/2 = 21 cm

• Area of ∆ = √ s(s - a)(s - b)(s - c)

$\leadsto \small \sf Area \:=\: \sqrt{21(21\:-\:18)(21\:-\:10)(21\:-\:14)}$

$\leadsto \small \sf Area \:=\: \sqrt{21(3)(11)(7)}$

$\leadsto \small \sf Area \:=\: \sqrt{4851}$

$\leadsto \small \sf Area \:=\: 69.65\:cm²$

• Area of Triangle = 69.65 cm²

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