Question

The perimeter of a triangle field is 450m it's side's are in the ratio 13:12:15.using herons formula find the area of triangle.

Answer 1

Hi
Let 1st side be 13x.
2nd side 12x.
3rd side 15x
Perimeter =450m
Semi perimeter = a+b+c \2
SO,
Semi perimeter = 13x+12x+15x \2
= 40\2
=20....

By herons formula...........

√s(s-a) (s-b) (s-c)
20 (20-13)(20-12)(20-15)
20 ×7 × 6×5
4200 app. Hope it help you

Answer 2

Answer:

$\large\underline\bold{GIVEN,}$

450m⇢Perimeteroftriangle=450m

⇢ratios of the sides of triangle sare

⇢13:12:5

FORMULA IN USE,

(herons fomula)

= s(s−a)(s−b)(s−c)

TO FIND,

⇢Area of triangle using herons formula.

SOLUTION,

$\therefore let\:the\:constant\:be\:'x'\:m∴let the constant be$

⇢sides of triangle are,

⇢a=13x

b=12x

c=5x

∴finding the value of x.

= a+b+c⇢perimeter of triangle=a+b+c

13x+12x+5x=450

⟹30x=450

⟹x= 30×450

$\implies x = \cancel\dfrac{450}{30}$

⟹x=15

⋆x=15⋆

b=12x

= 12\× 15 = 180m

c=5x

= 5× 15= 75m

⇢x=15

a=13x=13×15=195m

⇢b=12x=12×15=180m

⇢c=5x=5×15=75m

NOW, FINDING AREA OF TRIANGLE BY HERONS FORMULA,

$\therefore s= \dfrac{a+b+c}{2}$

∴s= 2

a+b+c

$\implies s= \dfrac{195+180+75}{2}$⟹

$\implies s= \dfrac{450}{2}$⟹

s= 2×450

$\implies s$= 225⟹s=225

)

= s(s−a)(s−b)(s−c)

$\implies \sqrt{225(225-195)(225-180)(225-75)}$⟹

225(225−195)(225−180)(225−75)

$\implies \sqrt{225(30)(45)(150)}$⟹

225(30)(45)(150)

$\implies \sqrt{ 225(1350)(150)}$⟹

225(1350)(150)

$\implies 15\sqrt{202500}$⟹15

202500

$\implies 15 \times 450$⟹15×450

$\implies 6750m^2$⟹6750m

2

$\large{\boxed{\bf{ \star\:\:area\:of\:triangle= 6750m^2 \:\: \star}}}$

⋆area of triangle=6750m

AREA OF TRIANGLE IS 6750m