Name: Finding area of triangle using base and height
Uploaded: 2019-07-19
Duration: 10 min 43 s
Description: Do you know that you can find the area of a triangle using its base and height? Well, that is what we'll learn about in this informative video. Learn more.

Question

The base of triangular field is three times its altitude. If the cost of sowing the field at $₹ 58$ per hectare is $₹ 783$ , find the length of the base and height in metre.

Accepted Answer

It is given that the base of the triangular field is three times its altitude.

Therefore, let us assume the height of the triangular field be $x$ and base be $3 x$ .

We know that,

Area of triangle $= \frac{1}{2} \times$ Base $\times$ Height

$= \frac{1}{2} \times 3 x \times x$

$= \frac{3}{2} x^{2} . . . . (1)$

We know that,

$1$ hectare $= 10, 000 m^{2}$

Rate of sowing the field per hectare $= ₹ 58$

Total cost of sowing the triangular field $= ₹ 783$

Therefore,

Total cost $=$ Area of the triangular field $\times ₹ 58$

$\Rightarrow ₹ 783 = Area \times ₹ 58 \Rightarrow Area = 13.5 hectare \Rightarrow Area = 13.5 \times 10000 m^{2} \Rightarrow Area = 135000 m^{2} . . . . . (2)$

Using $(2)$ in $(1)$ , we get,

$\begin{array}{rcl} \Rightarrow & 135000 m^{2} = \frac{3}{2} x^{2} \Rightarrow x^{2} = 9000 \Rightarrow x = 300 m \end{array}$

Hence, height of the triangular field $= x = 300 m$ .

Base of triangular field $= 3 x = 3 \times 300 = 900 m$ .

Therefore, the length of the base is $900 m$ and height of the field is $300 m$ .

The base of triangular field is three times its altitude. If the cost of sowing the field at $₹ 58$ per hectare is $₹ 783$ , find the length of the base and height in metre.

Important Questions on Perimeter and Area

Learn and Prepare for any exam you want !

The base of triangular field is three times its altitude. If the cost of sowing the field at ₹58 per hectare is ₹783, find the length of the base and height in metre.

Important Questions on Perimeter and Area

Learn and Prepare for any exam you want !

The base of triangular field is three times its altitude. If the cost of sowing the field at $₹ 58$ per hectare is $₹ 783$ , find the length of the base and height in metre.