Question

the ratio of length to breadth of a rectangular field is 4 is to 3 if diagonal is 200 the area of the field in square metres is

Answer 1

Given :-

• The ratio of length to breadth of a rectangular field is 4 : 3 if diagonal is 200m

To find :-

• Area of the field in m²

Solution :-

Let the length be 4x and breadth be 3x

• Diagonal of rectangle = 200m

As we know that

→ D = √l² + b²

Where " D " is diagonal, " l " is length and " b " is breadth.

As per given condition

→ D = √l² + b²

→ 200 = √(4x)² + (3x)²

→ 200 = √16x² + 9x²

→ 200 = √25x²

→ 200 = 5x²

→ x² = 200/5

→ x² = 40

→ x = √40

→ x = 6.32m approx

Hence,

• Length of rectangle = 4x = 25.28m
• Breadth of rectangle = 3x = 18.96m

Now,

→ Area of rectangle

→ Length × breadth

→ 25.28 × 18.96

→ 25.2 × 18.9

→ 476.28m²

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)?+ (Perpendicular)²

• (200)={4x)5 + (3x)4

• 40000 =16x+9x

• 40000 = 25x2

• 40000x²+25-x 1600

x=40m

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

• Now, we have to find the area of the field

• the area of the rectangular field,
• We use the formula:-

• Area of Rectangle = Length x+Breadth

According to question

• Area = 160 x 120

• Area = 19200 m2

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Hence, the area of rectangular field is 19200 m2

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