Question

The ratio of length to breadth of a rectangular field is 4:3. If it's diagonal is 200m then the area of the field

Answer 1

let l= 4x

let b= 3x

LOOK AT THE FIGURE GIVEN

from the figure

AC² =AB²+BC² (∠B= 90° SO PYTHAGORAS THEOREM)

200²= (4x)² +(3x)²(putting the values)

4000/25=x²

40 =x

thus sides are 3x=120m and 4x=160m

area = lxb

120 x 160 =19200m²

Answer 2

GIVEN:

• The ratio of length and breadth of a rectangular field is 4:3
• The diagonal of the rectangular field = 200 m

TO FIND:

• What is the area of the field ?

SOLUTION:

Let 'x' be the common in given ratios

• Length = 4x
• Breadth = 3x

☞ To find the Length and breadth of the rectangular field, we use the Pythagoras theorem

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

On putting the values in the formula we get

$\sf{\implies (200)^2 = (4x)^2 +(3x)^2 }$

$\sf{\implies 40000 = 16x^2 + 9x^2}$

$\sf{\implies 40000 = 25x^2 }$

$\sf{\implies x^2 = \cancel\dfrac{40000}{25} }$

$\sf{\implies x^2 = 1600 }$

$\bf{\implies x = 40\: m }$

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

Now, we have to find the area of the field

To find the area of the rectangular field, we use the formula:-

✬ Area of Rectangle = Length $\times$ Breadth ✬

According to question:-

$\sf{\implies Area = 160 \times 120}$

$\bf{\implies Area = 19200 \: m^2 }$

❝ Hence, the area of rectangular field is 19200 m² ❞

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