Question

please solve this..... it's urgent ​

Answer 1

Answer:

Area of ∆ABC = 30sq.cm

Step-by-step explanation:

perimeter of∆ABC &∆PQR is equal so,

side AB+5+13 = 6+14+10

=30=18+AB

30-18=AB

• side AB = 12 cm
• Area of ∆ABC = 1/2 × base × height
• A(∆ABC)= 1/2 × 5×12=60/2 =30

Answer 2

Answer:

• Area of ∆ABC is 30 sq units.

Step-by-step explanation:

Given :-

• Perimeter of ∆ABC is equal to perimeter of ∆PQR.
• Two sides of ∆ABC are 13 and 5.
• Three sides of ∆PQR are 6, 10 and 14.

To find :-

• Area of ∆ABC.

Solution :-

Let, Third side of triangle be x.

Perimeter of triangle = Sum of all sides

Perimeter of ∆ABC = Perimeter of ∆PQR

$\longrightarrow$ x + 13 + 5 = 6 + 10 + 14

$\longrightarrow$ x + 18 = 30

$\longrightarrow$ x = 30 - 18

$\longrightarrow$ x = 12

Thus,

Third side of ∆ABC is 12.

Here,

Height of triangle is not given.

So, we will use

Heron's formula that is :

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

Where,

• s is semi-perimeter of triangle.
• a, b and c are sides of triangle.

So, For ∆ABC :

Semi-perimeter = Perimeter of triangle/2

$\longrightarrow$ Semi-perimeter = 30/2

$\longrightarrow$ Semi-perimeter = 15

Semi-perimeter of triangle is 30.

Now,

$\longrightarrow$ Area = √15(15 - 12)(15 - 13)(15 - 5)

$\longrightarrow$ Area = √15 × 3 × 2 × 10

$\longrightarrow$ Area = √3 × 5 × 3 × 2 × 5 × 2

$\longrightarrow$ Area = 3 × 2 × 5

$\longrightarrow$ Area = 30

Therefore,

Area of ∆ABC is 30.