Question

The perimeter of atriangle is 450m and the sides are in the ratio 12:13:15. find the area using herons formula

Answer 1

☆Solution☆

Given =》

Perimeter = 450m

Sides are in ratio 12:13:15

Answer:-

Area = 150√6

Need to Find =》

Area=?

Explanation =》

Let first be 12x

Second be 13x

Third be 15x

Semi perimeter = 450/2 = 225m

we know that,

Perimeter of a triangle= Sum of all Sides

450= 12x+13x+15x

450= 30x

450/30=x

x= 15m

Hence, Sides are :-

12x= 12×15= 195m

13x= 13×15= 180m

15x=15×15= 225m

By Using Heron's Formula

Area of triangle =》 √[s( s-a)(s-b)(s-c)

$\sqrt{225(225 - 195)(225 - 180)(225 - 225)} \\ \\ = \sqrt{225 \times 30 \times 45 \times 1} \\ \\ = 15 \sqrt{30 \times 9 \times 5 \times 1} \\ \\ = 15 \times 3 \sqrt{30 \times 5} \\ \\ = 30 \sqrt{150} \\ \\ = 30 \sqrt{25 \times 6} \\ \\ = 30 \times 5 \sqrt{6} \\ \\ = 150 \sqrt{6}$

Area of triangle is 150√6

hope IT HELPs!!!

Answer 2

Step-by-step explanation:

☆Solution☆

Given =》

Perimeter = 450m

Sides are in ratio 12:13:15

Answer:-

Area = 150√6

Need to Find =》

Area=?

Explanation =》

Let first be 12x

Second be 13x

Third be 15x

Semi perimeter = 450/2 = 225m

we know that,

Perimeter of a triangle= Sum of all Sides

450= 12x+13x+15x

450= 30x

450/30=x

x= 15m

Hence, Sides are :-

12x= 12×15= 195m

13x= 13×15= 180m

15x=15×15= 225m

By Using Heron's Formula

Area of triangle =》 √[s( s-a)(s-b)(s-c)

√225(225−195)(225−180)(225−225)

$\sqrt225×30×45×1$

$15 \sqrt30×9×5×1$

$15×3 \sqrt 30×5$

$30 \sqrt 150$

$30 \sqrt25×6$

$30×5 \sqrt 6$

$150 \sqrt6$

★Area of triangle is 150√6★