Question

The lengths of the sides of a triangle are 5 cm, 12 cm and 13 cm. What is the area of this triangle?​

Answer 1

Answer:

30cm^2

Step-by-step explanation:

√s(s-a)(s-b)(s-c)

s=a+b+c÷2

13+5+12÷2

30÷2

15cm

√15(15-13)(15-5)(15-12)

√15*2*10*3

3×5×2×2×3

3×5×2×3

15×3

30cm^2

Answer 2

☯ Let the sides of triangle be a, b and c.

⠀⠀

$\frak{Given}\begin{cases} & \sf{a = \bf{5\;cm}} \\ & \sf{b = \bf{12\;cm}} \\ & \sf{c = \bf{13\;cm}}\end{cases}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$:\implies\sf s = semi - perimeter$

$:\implies\sf s = \dfrac{a + b + c}{2}$

$:\implies\sf s = \dfrac{5 + 12 + 13}{2}$

$:\implies\sf s = \dfrac{30}{2}$

$:\implies\bf s = 15$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

☯ Now, Finding area of triangle using Heron's Formula,

⠀⠀

$\star\;{\boxed{\sf{\purple{A = \sqrt{s(s - a)(s - b)(s - c)}}}}}$

$:\implies\sf A = \sqrt{(15 - 5)(15 - 12)(15 - 13)}$

$:\implies\sf A = \sqrt{15 \times 10 \times 3 \times 2}$

$:\implies\sf A = \sqrt{900}$

$:\implies{\boxed{\frak{\pink{A = 30\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\;triangle\;is\; \bf{30\;cm^2}.}}}$