Question

if the perimeter of a triangle is 42m and two sides are 17m and 13m. find the area of it.​

Answer 1

Answer:

• Area of triangle is 77.76 m².

Step-by-step explanation:

Given :-

• Perimeter of triangle is 42 cm.
• Two sides of triangle are 17 m and 13 m.

To find :-

• Area of triangle.

Solution :-

Let, Third side of triangle be x m.

Perimeter of triangle = Sum of all sides

$\longrightarrow$ 42 = 17 + 13 +x

$\longrightarrow$ 42 = 30 + x

$\longrightarrow$ 42 - 30 = x

$\longrightarrow$ x = 12

Measure of third side of triangle is 12 cm.

Here,

We will use Heron's formula because we do not have height of triangle.

Heron's formula 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,

Semi-perimeter = Perimeter/2

$\longrightarrow$ Semi-perimeter = 42/2

$\longrightarrow$ Semi-perimeter = 21

Semi-perimeter of triangle is 21 m.

Now,

$\sf \longrightarrow Area = \sqrt{21 \times (21 - 17)(21 - 13)(21 - 12)}$

$\sf \longrightarrow Area = \sqrt{21 \times 4 \times 8 \times 9}$

$\sf \longrightarrow Area = \sqrt{3 \times 7 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3}$

$\sf \longrightarrow Area = 3 \times 2 \times 2 \times \sqrt{3 \times 7 \times 2}$

$\sf \longrightarrow Area = 12 \times \sqrt{42}$

$\sf \longrightarrow Area = 12 \times 6.48$

$\sf \longrightarrow \bold{ Area = 77.76 }$

Therefore,

Area of triangle is 77.76 m².

Answer 2

Answer :-

• Area of triangle is 77.76 m².

Explanation :-

Given :

• Perimeter of triangle is 42 cm.
• Two sides of triangle are 17 m and 13 m.

To Find :

• Area of triangle.

Solution :

Let, Third side of triangle be x.

Perimeter of triangle = Sum of all sides

$\dashrightarrow$ 42 = 17 + 13 + x

$\dashrightarrow$ 42 = 30 + x

$\dashrightarrow$ 42 - 30 = x

$\dashrightarrow$ x = 12

• Measure of third side of triangle = 12 cm.

Now,

• We will use Heron's formula because we do not have height of triangle.

Heron's formula is :

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

Where,

• s = Semi-perimeter of triangle.

• a, b and c = Sides of triangle.

So,

Semi-perimeter = $\sf\dfrac{Perimter}{2}$

$\dashrightarrow$Semi-perimeter = $\sf\dfrac{42}{2}$

$\dashrightarrow$ Semi-perimeter = 21

• Semi-perimeter of triangle = 21 m.

Now,

$\sf \dashrightarrow {\sqrt{21 \times (21 - 17)(21 - 13)(21 - 12)}}$

$\sf \dashrightarrow {\sqrt{21 \times 4 \times 8 \times 9}}$

$\sf \dashrightarrow {\sqrt{3 \times 7 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3}}$

$\sf \dashrightarrow {3 \times 2 \times 2 \times \sqrt{3 \times 7 \times 2}}$

$\sf \dashrightarrow {12 \times \sqrt{42}}$

$\sf \dashrightarrow{12 \times 6.48}$

$\dashrightarrow{\underline{\boxed{\textsf{\textbf{\red{77.76}}}}}}$

Therefore,

• Area of triangle = 77.76 m².