Question

A triangle shaped land has the sides in the ratio 3:5:7, if its perimeter is 300 meter. What will be the area of the land
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Answer 1

Given :-

• Side ratio of Triangle shaped land = 3 : 5 : 7 .
• Perimeter of land = 300m .

To Find :-

• Total area of land ?

Solution :-

Let us assume that, sides of Triangle shaped land are 3x, 5x and 7x respectively.

Than,

→ Perimeter of land = sum of all sides.

→ 3x + 5x + 7x = 300

→ 15x = 300

→ x = 20.

Therefore,

→ First side = 3x = 3*20 = 60m.

→ second side = 5x = 5*20 = 100m.

→ Third side = 7x = 7*20 = 140m.

Now,

→ By Heron's formula area of ∆ with three sides as a,b and c and semi - perimeter as s is :-

• √{s(s-a)(s-b)(s-c)}

So,

→ semi-perimeter of land = (Perimeter/2) = (300/2) = 150m.

Putting all values now in Heron's formula we get :-

→ Area = √{150 * (150-60) * (150 - 100) * (150 - 140)}

→ Area = √{150 * 90 * 50 * 10}

→ Area = √{3 * 50 * 3 * 30 * 50 * 10}

→ Area = √{(3)² * (50)² * 3*(10)²}

→ Area = 3 * 50 * 10 * √3

→ Area = 1500√3 m².

Hence, Area of Land is 1500√3m².

Answer 2

Answer:

Step-by-step explanation:

HELLI DEAR,

The side of triangular shaped land are in ratio 3:5:7.

Let be x be the number.

So, lengh of each side 3x , 5x ,7x.

Perimeter of triangle 3x + 5x + 7x= 15x

And perimeter is given = 300 meter.

So, 15x = 300 m

x= 300/15

x= 20 m.

Each side lengh of triangle,

3x = 3×20 = 60 m

5x= 5× 20= 100 m

7x= 7× 20 = 140 m.

Length of three sides of a triangle are 60 m , 100 m, 140 m.

So, area is find by using Herons formula.

Area of tri ABC = √{ s(s-a)(s-b)(s-c)}

where s = semiperimeter of triangle .

So s= 300/2 = 150m

Area of tri ABC = √{150(150-60)(150-100)(150-140)}

=>√{150(90)(50)(10)}

=>√{150×90×500}

=>√{2×3×5×5×2×3×3×5×2×2×5×5×5}

=>2×2×3×5×5×5√3

=>1500√3 m square. Answer.

I HOPE IT HELP YOU DEAR,

THANKS