Question

Question for mods
Three sides of a triangle measure 8 m ,15 m,17 m. Find its area and Perimeter

Answer 1

Given :

Three sides of a triangle measure 8 m ,15 m & 17 m.

To find :

• Area and perimeter of trianlge

Solution :

Triangle measures = 8m, 15m & 17 m

According to the heron's formula

→ s = ½(a + b + c) where " s " is the semiperimeter

• a = 8m
• b = 15m
• c = 17m

→ s = ½(8 + 15 + 17)

→ s = ½ × 40

→ s = 20 m

★ Area of trianlge=√s(s - a)(s - b)(s - c) ★

→ √20(20 - 8)(20 - 15)(20 - 17)

→ √20 × 12 × 5 × 3

→ √20 × 60 × 3

→ √3600

→ 60 m²

•°• Area of a triangle = 60m²

________________________________

Perimeter of a trianlge = Sum of three sides of a triangle

→ 8 + 15 + 17

→ 40 m

•°• Perimeter of a triangle = 40 m

________________________________

Answer 2

$\huge\mathcal\purple{\underline{Given :}}$

$\mathrm{Measures \: of \: the \: triangle \: 8m, \: 15m, \: 17m}.$

$\huge\mathcal\green{\underline{To\: Find:}}$

$\mathrm{Area \: and \: perimeter \: of \: the \: triangle.}$

$\huge\mathcal\blue{\underline{Sollution:}}$

$\mathrm{\underline{Let \: a = 8, \: b = 15, \: c = 17}}$

$\mathrm{perimeter = a + b + c}$

$\implies\mathrm{ 8 + 15 + 17}$

$\implies\mathrm\red{\underline{ 40m}}$

$\mathrm{\underline{Area \: of \: triangle \: using \: herons \: formula,}}$

$\mathrm{s = \frac{a + b + c}{2} = \frac{8 + 15 + 17}{2} = \frac{40}{2}}$

$\implies\mathrm{s = 20m}$

$\mathrm{now \: calculating \: area}$

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

$\implies\mathrm{\sqrt{20(20 - 8)(20 - 15)(20 - 17)} }$

$\implies \mathrm{\sqrt{20(12)(5)(3)}}$

$\implies \mathrm{\sqrt{20(180)}}$

$\implies\mathrm{ \sqrt{3600}}$

$\implies\mathrm\red{\underline{60 \: m ^{2} }}$

$\mathrm\purple{therefore \: the \: perimeter \: is \: 40m \: and \: area \: is \: 60m^{2}}$