Question

The base of a triangular field is 2.4 times its height. If
the cost of levelling the field at the rate of 20 per
square meter is 9600; find its base and height.​

Answer 1

Step-by-step explanation:

area=9600÷20=480

let height be x unit.

base=2.4x

acc. to right angle triangle

1/2×2.4x×x=480

x=20unit

height=20

base=2.4×20=48

Answer 2

• The base of the triangle is given that 2.4 times the height of the triangle ✓

✓ But, we don't know the measure of the height of the triangle so let us take the base be x

$\bold{let \: the \: height\: be \: x \: m ^{2} }$

$\bold{and \: the \: base \: be \: (2.4 \times x \: )m ^{2} }$

Now , It is given the total costing for leveling throughout the area of the triangle is Rs 9600 and also given 1 m² = Rs 20 ( for leveling the area) ✓

So ,if we will divide the area total costing by the costing of 1 m² then we will get the area if the triangle which is as follows ✓

$\boxed{ \red{ \bold{area \: of \: the \: triangle = \frac{9600}{20} = 480m^{2} }}}$

so

Now , we can see the area of the triangle is = 480 m²

•°•

$= > x \times 4.2x = 480 \\ \\ = > 4.2x^{2} = 480 \\ \\ = > x^{2} = \frac{480}{4.2} \\ \\ = > x ^{2} = \frac{4800}{42} \\ \\ = > x ^{2} = 114.2$

$x = \sqrt{114.2} \\ \\ = > x = 10.6 \: m$

so from the above calculation we find the height of the triangle is 10.6 m

•°• base = 10.6×4.2= 44.52 m

$\boxed{ \red{ \bold{height = 10.6 m\: and \: base =44.52 \: m }}}$