Question

Find the area of the triangle with sides 21 cm, 16 cm and 13 cm. Also, find the perimeter of an equilateral
triangle equal in area to this triangle.​

Answer 1

$\fbox\green{Answer}$

Find the perimeter of an equilateral triangle whose area is equal to that of a triangle with sides 21cm 16cm and 13cm.

Step by step explanation :

As per your question,

Area of an equilateral triangle = Area of triangle with sides 21cm, 16 cm and 13 cm... (1)

Now,

Let's find the Area of triangle with given sides.

We know that,

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

$\tt{= \frac{21 + 16 + 13}{2}}$

$\tt{ = \frac{50}{2}}$

$\tt{ = 25}$

Using Heron's Formula,

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

$\tt \small {= \sqrt{25(25 - 21)(25 - 16)(25 - 13)}}$

$\tt{ = \sqrt{25 \times 4 \times 9 \times 12}}$

$\tt{= 60 \sqrt{3}}$

Thus, Area = 60√3.

Now,

$\small \tt{Area \: of \: equi. \: triangle = \frac{ \sqrt{3} }{4} \times {a}}^{2}$

From (1) ,

$\tt{\frac{ \sqrt{3} }{4} {a}^{2} = 60 \sqrt{3}}$

Cancelling √3 on both sides,

$\tt {\frac{ {a}^{2} }{4} = 60}$

$\tt{{a}^{2} = 60 \times 4}$

$\tt{a = \sqrt{240}}$

a = 4√15

Thus, Side of the equilateral triangle is 4√15 cm.

Now, We have to find the perimeter.

$\tt \small{Perimeter \: of \: triangle = 3a}$

$\tt{= 3 \times 4 \sqrt{15}}$

$\tt {= 12 \sqrt{15}}$

Thus,

Perimeter of the equilateral triangle is 12 √15.

Answer to the question is 12√15.

Answer 2

Find the perimeter of an equilateral triangle whose area is equal to that of a triangle with sides 21cm 16cm and 13cm.

• Perimeter of the equilateral triangle is 12 √15.
• Answer to the question is 12√15.