Question

The perimeter of a triangular field is 144m and the ratio of the sides is 3:4:5, then the area of the field is

a) 864sq m

b) 764sqm

c) 854sqm

d) 754sqm

Answer 1

Answer:

Let the sides be denoted as 3x, 4x and 5x

Then 3x+4x+5x = 144 which gives x = 12m

So, sides of the triangle are 36m, 48m and 60m.

Also, s = 144/2 = 72m

Using Heron's formula, Area = √s(s-a)(s-b(s-c)

= √72(72-36)(72-48)(72-60)

= √72×36×24×12

= √6×4×3×6×6×6×4×4×3

= 6×6×4×3×2

= 864sq m

Answer 2

${\bold{\pink{\underline{\green{G}\purple{iv}\orange{en}\red{:-}}}}}$

• Perimeter = 144 m

• Ratio of the sides = 3:4:5

${\bold{\pink{\underline{\pink{To}\:\purple{Fin}\blue{d}\red{:-}}}}}$

• Area of the field = ?

${\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

Let the sides of triangular field be 3x,4x and 5x

A/q,

3x + 4x + 5x = 144

12x = 144

x = 144/12

x = 12 m

Now,

Sides are ,3x = 3 × 12 = 36 m

4x = 4 × 12 = 48 m

5x = 5 × 12 = 60 m

Now we have a = 36m, b = 48m , c = 60m

we know that

Semi perimeter = a + b + c / 2

Semi perimeter = 36 + 48 + 60/2

Semi perimeter = 144/2

Semi perimeter = 72m

$\bf\boxed\star\red{\underline{\underline{{Using\:Heron's\:Formula}}}}$

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

Area=$\bf\:\sqrt{72(72-36)(72-48)(72-60)}$

Area=$\bf\:\sqrt{72\times\:36\times\:24\times\:12}$

Area=$\bf\:\sqrt{746496}$

Area= 864 m²

Hence Area of field is 864 m²

So, Option (a) 864 sq m is correct