Question

A triangular plot is being constructed having its base twice to its altitude. What will be
the base and altitude of the plot if the cost of levelling it at the rate of ₹25 per square
meter is ₹11,025.

Answer 1

Answer:

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

• According to the Question Now :

\begin{gathered}:\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\end{gathered}

:⟹Total Cost = Area of Triangle × Rate of Leveling

:⟹Rs.11025=Area×Rs.25m

−2

:⟹

Rs.25m

−2

Rs.11025

=Area

:⟹AreaofTriangle=441m

2

†AreaofTriangle=

2

1

×Base×Height

:⟹

2

1

×Base×Height=441m

2

:⟹

2

1

×

2

n×n=441m

2

:⟹n×n=441m

2

:⟹n

2

=441m

2

:⟹n=

441m

2

:⟹n=

21m×21m

:⟹n=21m

\rule{220}{2}

• 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.