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 Do it With Proof a) 18200 b) 19200 c) 18500 d) 18900
Answers
Answer:
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}⟼Letlengthofthefieldbe=4x
\longmapsto\tt{Let\:breadth\:of\:the\:field\:be=3x}⟼Letbreadthofthefieldbe=3x
Using Formula :
\longmapsto\tt\boxed{Diagonal=\sqrt{{(l)}^{2}+{(b)}^{2}}}⟼
Diagonal=
(l)
2
+(b)
2
Putting Values :
\longmapsto\tt{200=\sqrt{{(4x)}^{2}+{(3x)}^{2}}}⟼200=
(4x)
2
+(3x)
2
\longmapsto\tt{200=\sqrt{{16x}^{2}+{9x}^{2}}}⟼200=
16x
2
+9x
2
\longmapsto\tt{200=\sqrt{{25x}^{2}}}⟼200=
25x
2
\longmapsto\tt{200=5x}⟼200=5x
\longmapsto\tt{\cancel\dfrac{200}{5}=x}⟼
5
200
=x
\longmapsto\tt\bf{40=x}⟼40=x
Value of x is 40 .
Therefore :
\longmapsto\tt{Length\:of\:field=4(40)}⟼Lengthoffield=4(40)
\longmapsto\tt\bf{160\:m}⟼160m
\longmapsto\tt{Breadth\:of\:field=4(30)}⟼Breadthoffield=4(30)
\longmapsto\tt\bf{120\:m}⟼120m
For Area :
Using Formula :
\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{b}}⟼
AreaofRectangle=l×b
Putting Values :
\longmapsto\tt{160\times{120}}⟼160×120
\longmapsto\tt\bf{19200\:{m}^{2}}⟼19200m
2
Option b) 19200 is Correct .