Question

The ratio of length to breadth of a rectangular field is 4:3. if it's diagonal is 200m. the area of the field in square meters.​

Answer 1

Answer:

mention weather 200 meter is length or breahth

Answer 2

Given :-

The ratio of length to breadth of a rectangular field = 4 : 3

Diagonal of the rectangular field = 200 m

To Find :-

The length of the rectangle.

The breadth of the rectangle.

The area of the field in square meters.​

Solution :-

Given that,

Ratio is 4 : 3 and it's diagonal is 200 m

First, we have to find the length and breadth of the rectangle.

Let us consider the length and breadth to be 4x and 3x respectively.

By the Pythagoras theorem,

$\underline{\boxed{\sf (Hypotenuse)^{2}=(Base)^{2}+(Perpendicular)^{2}}}$

Substituting their values, we get

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

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

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

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

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

$\sf =x=\sqrt{1600}$

$=\sf x =40 \ m$

Hence, the value of x is 40 m

Length = $\sf 4x=4 \times 40$

$\longrightarrow \sf 160 \ m$

Breadth = $\sf 3x=3 \times 40$

$\longrightarrow \sf 120 \ m$

Therefore, the length and breadth is 160 m and 120 m respectively.

Now, finding the area

$\underline{\boxed{\sf Area \ of \ a \ rectangle= Length \times Breadth}}$

Substituting their values,

Area of the rectangle = $\sf 160 \times 120$

$\longrightarrow \sf 19200 \ m^{2}$

Therefore, the area of the rectangle is 19200 m²