Question

The ratio of the sides of a triangular land is 5:12:13. If the area of the land be 900 sqm, find its perimeter [hint: use area = root over s×(s-a)×(s-b)×(s-c)]​

Answer 1

Answer:

164.4 m

Step-by-step explanation:

Let the sides of the land be of lengths 5x m, 12x m, 13x m.

Semi-perimeter of the land is

$\frac{5x + 12x + 13x}{2} \\\frac{30x}{2} \\15x$

Given,

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

$900 = \sqrt[]{15x(15x-5x)(15x-12x)(15x-13x)} \\900 = \sqrt[]{15x X10xX3xX2x} \\900 = \sqrt{900x^{4} }\\900 = 30x^{2} \\or, x^2 = \frac{900}{30} \\or, x^2 = 30\\or, x = 5.48 (approx.)$

The perimeter of field

= 30x m

= (30 × 5.48) m

= 164.4 m

PLEASE MARK BRAINLIEST...

Answer 2

Step-by-step explanation:

Perimeter of triangle =150m (given)

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

On dividing 150 m in the ratio 5:12:13, we get

a=5xcm

b=12xcm

c=13xcm

we know that, perimeter of a triangle = Sum of all sides =a+b+c

150=5x+12x+13x

150=30x

x=5

Sides are:

a=5x=25cm

b=12x=60cm

c=13x=65cm

Now,

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

Apply Heron's Formula of find the area of triangle.

Area =S(S−a)(S−b)(S−c)

Where S=2a+b+c

S=21(25+60+65)=75cm

Area =(75(75−20)(75−60)(75−65))

         =(75×50×15×10)

         =750

Area of triangle is 750cm2.