Question

the ratioof lenght to breadth of a rectangular Field is4:3. If it's diagonal is 200m, the area of the field in s​

Answer 1

Given:

The ratio of length and breadth of a rectangular field is 4:3

The diagonal of the rectangular field = 200 m

Find:

Area of the field

Solution:

Let 'x' be the common in given ratios

Length = 4x

Breadth = 3x

Pythagoras theorem:-

(Hypotenuse)² = (Base)² + (Perpendicular)²

=> (200)² = (3x)² + (4x)²

=> 40000 = 9x² + 16x²

=> 40000 = 25x²

=> 40000/25 = x²

=> 1600 = x²

=> √1600 = x²

=> 40 = x

=> x = 40

So,

• Length = 4x = 4(40) = 160
• Breadth = 3x = 3(40) = 120

Now,

Area of Rectangle = Length × Breadth  

=> 160 ×120

=> 19200m²

Hence, the area of rectangular field is 19200 m².

I hope it will help you.

Regards.

Answer 2

let the length and breadth be 4x and 3x respectively .

According to the question

diagonal = √ l²+b²

200= √(4x)²+(3x)²

200 = √16x²+9x²

200 = √25x²

200= 5x

x= 200/5 = 40

x= 40

hence length and breadth are 4x = 4×40 = 160 and 3x = 3×40 = 120m respectively.

Area of rectangle =

length×breadth

= 160×120

= 19200cm²