Question

Two sides of a triangle are of length 5
cm and 12 cm. If its perimeter is 30
cm. The area of triangle is​

Answer 1

[HeY Mate]

$\huge\bold\red{Answer}$

Given,

• Side 1 = 5cm.
• Side 2 = 12cm.
• Perimeter = 30cm.

To Find,

• Area of triangle?

Solution:

$\tt perimeter \: of \: triangle = 30cm \\ \tt 5m + 12cm + 3rd \: side = 30cm \\ \tt 3rd \: side = 30cm - 17cm \\ \tt 3rd \: side = 13cm.$

Now, We will use Heron's Formula,

$\tt s \implies \frac{a + b + c}{2} \\ \tt s = \frac{5 + 12 + 13}{2} \\ \tt s = \frac{30}{2} \\ \tt s= 15$

$\tt area \: of \: triangle = > \sqrt{s(s - a)(s - b)(s - c)} \\ \tt = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} \tt \\ \tt = \sqrt{15(10)(3)(2)} \\ \tt = \sqrt{15(60)} \\ \tt = \sqrt{900} \\ \tt = 30cm {}^{2}$

I Hope It Helps You✌️

Answer 2

Given :

• Side of triangle ( a ) = 5 cm

• Side of triangle ( b ) = 12 cm

• Perimeter of triangle = 30 cm

To Find :

• Area of the triangle

Solution :

• Fisrt we have to find third side ( c ) of the triangle

$\implies \boxed{ \sf \red{ Perimeter = a + b + c}} \\ \\ \sf \implies30 = 5 + 12 + c \\ \\ \sf \implies30 = 17 + c \\ \\ \sf \implies 30 - 17 = c \\ \\\sf \implies c = 13$

Now Semi-perimerter of the triangle

$\implies \boxed{\sf \green{s = \frac{a + b + c}{2}}} \\ \\ \sf \implies s = \frac{5 + 12 + 13}{2} \\ \\\sf \implies s = \frac{30}{2} \\ \\ \sf \implies s =15$

By using Heron's formula

$\large \boxed{\boxed{\sf \blue{Area_{triangle} = \sqrt{s(s - a)(s - b)(s - c)}}}} \\ \\ \sf \implies \sqrt{15(15 - 5)(15 - 12)(15 - 13)} \\ \\\sf \implies \sqrt{15 \times 10 \times 3 \times 2} \\ \\ \sf \implies \sqrt{900}\\ \\ \sf \implies30 \\ \\ \large\implies \boxed{ \boxed{ \sf \orange{ Area_{triangle} =30 \: {cm}^{2}}}}$