The base of a triangular field is three times its height and its area is 1350 m2.

Question:

The base of a triangular field is three times its height and its area is 1350 m2. Find the base and height of the field.

Solution:

Let the base of the triangular field be $3 x \mathrm{~cm}$ and its height be $x \mathrm{~cm}$.

Then, area of the triangle $=\left(\frac{1}{2} \times 3 x \times x\right) m^{2}$

$=\frac{3 x^{2}}{2} \mathrm{~m}^{2}$

But it is given that the area of the triangular field is $1350 \mathrm{~m}^{2}$.

$\therefore \frac{3 x^{2}}{2}=1350$

$\Rightarrow x^{2}=\left(1350 \times \frac{2}{3}\right)$

$\Rightarrow x^{2}=900$

$\Rightarrow x=\sqrt{900}$

$\Rightarrow x=30 m$

Hence, the height of the field is $30 \mathrm{~m}$.

$I$ ts base $=(3 \times 30) \mathrm{m}=90 \mathrm{~m}$

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