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

Answer:

Step-by-step explanation:

sum of sides = 21cm+16cm+13cm = 50cm = s

s/2 = 25

By Heron's formula:

$\sqrt{(s)(s-a)(s-b)(s-c)}\\= \sqrt{(25)(25-21)(25-16)(25-13)}\\= \sqrt{(25)(4)(9)(12)}\\\\= 5*2*3 *2\sqrt{3}\\= 60\sqrt{3} cm^2$

Area of equilateral triangle: = $\frac{\sqrt{3}}{4}a^2$

$\frac{\sqrt{3}}{4}a^2 = 60\sqrt{3}\\a^2 = 240\\a = 4\sqrt{15}$

Perimeter:

$=3a\\= 3 * 4\sqrt{15}\\=12 \sqrt{15}cm$

Answer 2

Answer:

Answer:

Step-by-step explanation:

sum of sides = 21cm+16cm+13cm = 50cm = s

s/2 = 25

By Heron's formula:

$\begin{gathered}\sqrt{(s)(s-a)(s-b)(s-c)}\\= \sqrt{(25)(25-21)(25-16)(25-13)}\\= \sqrt{(25)(4)(9)(12)}\\\\= 5*2*3 *2\sqrt{3}\\= 60\sqrt{3} cm^2\\\end{gathered}$

Area of equilateral triangle: = $\frac{\sqrt{3}}{4}a^2$

$\begin{gathered}\frac{\sqrt{3}}{4}a^2 = 60\sqrt{3}\\a^2 = 240\\a = 4\sqrt{15}\\\end{gathered}$

Perimeter:

$\begin{gathered}=3a\\= 3 * 4\sqrt{15}\\=12 \sqrt{15}cm\end{gathered}$