Question

the base of a triangular plot is twice of it height. if the cost of levelling it at the rate of ruppees 25 square meter is ruppees 11,025 find the base and the height of the plot​

Answer 1

AnswEr :

Let the Height be n, & Base be 2n i.e. (twice of its height).

• According to the Question Now :

$:\implies\textsf{Total Cost = Area of Triangle \times Rate of Leveling}\\\\\\:\implies\sf Rs. \:11025 = Area \times Rs.\:25\:{m}^{ - 2}\\\\\\:\implies\sf \cancel\dfrac{Rs. \:11025}{Rs. \:25\:{m}^{ - 2}} = Area\\\\\\:\implies\sf Area\:of \:Triangle = 441\:{m}^{2}\\\\ \quad\scriptsize{\bf{ \dag}\:\tt Area \:of \:Triangle = \dfrac{1}{2} \times Base \times Height}\\\\:\implies\sf \dfrac{1}{2} \times Base \times Height = 441 \:{m}^{2}\\\\\\:\implies\sf \dfrac{1}{ \cancel2} \times \cancel2n \times n = 441 \:{m}^{2}\\\\\\:\implies\sf n \times n = 441\:{m}^{2}\\\\\\:\implies\sf {n}^{2} = 441\:{m}^{2}\\\\\\:\implies\sf n= \sqrt{441\:{m}^{2}}\\\\\\:\implies\sf n = \sqrt{21 \:m \times 21 \:m}\\\\\\:\implies\sf n = 21\:m$

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• D I M E N S I O N S :

◗ Height = n = 21 m

◗ Base = 2n = 2(21 m) = 42 m

⠀

∴ Hence, Base and Height of the Triangle will be 42 m and 21 m respectively.

Answer 2

$\bf{\Huge{\boxed{\sf{\green{ANSWER\::}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}}$

The base of a triangular plot is twice of it height.If the cost of levelling  it at the rate of Rs.25m² is Rs.11025.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The base and the height of the plot.

$\bf{\Large{\underline{\sf{\red{Explanation\::}}}}}$

Let the base of a triangular plot be 2R.

Let the height of a triangular plot be R.

$\bf{We\:have}\begin{cases}\rm{Cost\:of\:levelling\:plot\:=\:Rs.11025}\\ \rm{The\:rate\:rate\:of\:plot\:=\:Rs.25m^{2} }\end{cases}}$

A/q

$\longmapsto\sf{Area\:of\:triangular\:plot\:=\:\frac{Cost\:of\:levelling\:plot}{Rate\:of\:plot} }$

$\longmapsto\sf{Area\:of\:triangular\:plot\:=\:\cancel{\frac{Rs.11025}{Rs.25 } }}$

$\longmapsto\sf{\red{Area\:of\:triangular\:plot\:=\:441m^{2} }}$

__________________________________

We know that formula of the area of triangle:

$\bf{\Large{\boxed{\tt{Area\:of\:triangle\:=\:\frac{1}{2} *Base*Height}}}}}$

Therefore,

$\mapsto\sf{441\:=\:\frac{1}{2} *2R*R}$

$\mapsto\sf{441\:=\:\frac{1}{\cancel{2}} *\cancel{2}R*R}$

$\mapsto\sf{441\:=\:R*R}$

$\mapsto\sf{441\:=\:R^{2} }$

$\mapsto\sf{\sqrt{441} \:=\:R}$

$\mapsto\sf{\red{21m\:=\:R}}$

Thus,

$\bf{\Large{\boxed{\rm{The\:base\:of\:triangular\:plot\:is\:2(21)\:=42m}}}}}$

$\bf{\Large{\boxed{\rm{The\:Height\:of\:triangular\:plot\:is\:\:21m.}}}}}$