Question

The Ratio of Length To Breadth of a Rectangular Field is 4 : 3. If Its Diagonal is 200 m, The Area of The Field in square meters ?​

Answer 1

Given :)

• The Ratio of Length To Breadth of a Rectangular Field is 4 : 3.
• Diagonal of Rectangle is 200 m.

To Find :)

• Area of field.

Solution :)

$\longmapsto\tt{Let\:length\:of\:the\:field\:be=4x}$

$\longmapsto\tt{Let\:breadth\:of\:the\:field\:be=3x}$

Using Formula :)

$\longmapsto\tt\boxed{Diagonal=\sqrt{{(l)}^{2}+{(b)}^{2}}}$

Putting Values :)

$\longmapsto\tt{200=\sqrt{{(4x)}^{2}+{(3x)}^{2}}}$

$\longmapsto\tt{200=\sqrt{{16x}^{2}+{9x}^{2}}}$

$\longmapsto\tt{200=\sqrt{{25x}^{2}}}$

$\longmapsto\tt{200=5x}$

$\longmapsto\tt{\cancel\dfrac{200}{5}=x}$

$\longmapsto\tt\bf{x=40}$

• Value of x is 40

Therefore :)

$\longmapsto\tt{Length\:of\:field=4(40)}$

$\longmapsto\tt\bf{160\:m}$

$\longmapsto\tt{Breadth\:of\:field=4(30)}$

$\longmapsto\tt\bf{120\:m}$

For Area :)

• Using Formula :-

$\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{b}}$

Putting Values :)

$\longmapsto\tt{160\times{120}}$

$\longmapsto\tt\bf{19200\:{m}^{2}\:Ànswer}$

• @Okhey

Answer 2

Step-by-step explanation:

L:B :: 4x:3x

so by pythagorus

diagonal will be= √ (16x^2+9x^3)

= √25x^2

5x

now 5x= 200

x= 200/5

x= 40

so,

length= 4×40=160m

breast=3×50=120m

Area =L×B

= 160m×120m

19200 square meter