Question

an isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle
3√5 cm²
9 √15 cm²
15 cm²
5 √3 cm²​

Answer 1

Given :

• Perimeter of Isosceles Triangle is 30cm and two equal sides each of 12cm.

To Find :

• Area of the Isosceles Triangle.

Solution :

• a = 12cm.
• b = 12cm.
• c = ?

$\longmapsto\tt{a+b+c=30}$

$\longmapsto\tt{12+12+c=30}$

$\longmapsto\tt{c=30-24}$

$\longmapsto\tt{c=6cm.}$

Now ,

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{12+12+8}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{30}{2}}$

$\longmapsto\tt\bold{s=15cm}$

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{15(15-12)(15-12)(15-6)}}$

$\longmapsto\tt{\sqrt{15\times{3}\times{3}\times{9}}}$

$\longmapsto\tt{\sqrt{5\times{3}\times{3}\times{3}\times{3}\times{3}}}$

$\longmapsto\tt{3\times{3}\sqrt{5\times{3}}}$

$\longmapsto\tt\bold{9\sqrt{15}{cm}^{2}}$

So , The Area of Isosceles Triangle is 9√15cm²..