Question

if the sidesof the triangle are in the ratio 5:12:13 and it's perimeter is 450m find its area
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Answer 1

Solution

Given :-

• The sides of the triangle are in the ratio 5:12:13
• perimeter of triangle = 450 m

Find :-

• Area of triangle

Explanation

Let,

• Side of triangle be = 5x , 12x , 13x

Using Formula

★ Perimeter of triangle = Sum of all sides

==> Perimeter of triangle = 5x + 12x + 13x

==> 450 = 30x

==> x = 450/30

==> x = 15

Since,

• First side will be = 5x = 5 * 15 = 75 m
• Second side will be = 12x = 12 * 15 = 180 m
• Third Side will be = 13x = 13 * 15 = 195 m

_________________________

Now Calculate Area

Suppose ∆ABC here,

Where,

• AB = 75 m
• BC = 180 m
• CA = 195 m

Calculate Area by Heron's Formula

★ Semi - perimeter (S) = (AB + BC + CA)/2

Keep all above Valuea

==> Semi - perimeter(S) = ( 75+180+195)/2

==> Semi - perimeter(S) = (450/2)

==> Semi - perimeter(S) = 225 m

Now, Using Heron's Formula

★ Area = √[S(S-AB)(S-BC)(S-CA)]

Keep all above values

==> Area = √[225(225-75)(225-180)(225-195)]

==> Area = √[225*150*45*30]

==> Area = √[15*15*15*10*15*3*15*2]

==> Area = 15 * 15 √(15*10*2*3)

==> Area = 225√(15*15*2*2)

==> Area = 225 * 15 * 2

==> Area = 6750 m²

Hence

• Area of triangle will be 6750 m²

_________________

Answer 2

Solution

Given =》

Perimeter = 450m

Sides in ratio 5:12:13

Answer =》

6750m²

To find =》

Area of triangle?

Explanation =》

Let first side be 5x

Second = 12x

Third = 13x

We know that ,

Perimeter = sum of all sides

450= 5x + 12x+ 13x

450 = 30x

x= 450/30

x= 15

Now, put x= 15 in all sides

5x= 5×15= 75

12x= 12×15= 180

13x= 13×15= 195

First side = 75m

Second side= 180m

Third side= 195m

For Semi Perimeter = Sum of all sides/2

75+180+195/2

450/2

= 225

Now , we using heron's formula

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

put the values

$\sqrt{225(225 - 75)(225 - 180)(225 - 195)} \\ \\ = \sqrt{225 \times 50 \times 45 \times 30} \\ \\ = \sqrt{45562500} \\ \\ = 6750m {}^{2}$

Hence, area of triangle = 6750m²