Math, asked by XxCuteAngelxX, 7 months ago

A farmer has a triangular field with sides 360m 200m and 240m where he grows wheat Adjacent to this field he has another triangular field with sides 240 m, 320 m and 400 m, divided into two parts by joining the midpoint of the
longest side to the opposite vertex. He grows potatoes in one part and onions in the other part. How much area (in hectares) has been used
for wheat, potatoes and onions?

(1 hectare = 10000 m.)

Help me out with it.

❣◾⬛Thank you⬛◾❣

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Answers

Answered by princethakur1613

Answer:

Area for Potatoes Cultivation = 1.92 Hectare

Area for Onion Cultivation = 1.92 hectare

Area for Wheat Cultivation = 2.26 Hectare

Step-by-step explanation:

The sides of the given triangles are:

Wheat cultivation - 240 m, 200 m and 360 m

We use Herons Formula to solve this problem:

Semi - Perimeter = (240 + 200 + 360) / 2

=> 400

Now,

Finding Area by using Herons Formula:

=>\sqrt{400(400-240)(400-200)(400-360)}=>

400(400−240)(400−200)(400−360)

=>\sqrt{(400)(160)(200)(40)}=>

(400)(160)(200)(40)

=>16000\sqrt{2}m^{2}=>16000

Converting Meter to Hectare:

1 Meter = 1 / 10,000 Hectare

=>16000\sqrt{2}m^{2}=>16000

/ 10,000

=>1.6\sqrt{2} hectare=>1.6

hectare

=> 1.6 * 1.414 (Substituting the value of \sqrt{2}

as 1.414)

=> 2.26 Hectare (approx.)

Area of the other Triangle which has the side measures as:

=> 240 m, 320 m and 400 m

These measures are for calculating area required for Onions and Potatoes cultivation.

Again we use Herons Formula here:

Semi - Perimeter = (240 + 320 + 400) / 2 = 480

Area required for Onions and Potatoes\sqrt{(480)(240)(160)(80)}

(480)(240)(160)(80)

=>\sqrt{(480)(240)(160)}=>

(480)(240)(160)

= 38,400 m²

Again Converting Meters to Hectares:

=> 38,400 / 10,000

=> 3.84 Hectares

Now, we divide the field into two parts by joining the mid - point of the longest side to the opposite vertex the Median as per the question. Median of a triangle divides the triangle into two equal parts and therefore the area of these equal parts will also be equal.

=> 3.84/2

=> 1.92 Hectare

Therefore, the final answer is as follows:

Area required for Potatoes Cultivation = 1.92 Hectares.

Area required for Onions Cultivation = 1.92 Hectares.

Area required for Wheat Cultivation = 2.26 Hectares.

Answered by XxMissPaglixX

${\huge{\mathtt{\red{AnSwEr:-}}}}$

$<body bgcolor="black"><font color="green">$

Let ABC be the field where wheat is grown. Let ACD be the field which is divided into two parts by joining C to the midpoint E of AD.

For /\ ABC, we have

$a = 200m \: b = 240m \: and \: c = 360m. \\$

$s = \frac{1}{2} (200 + 240 + 360)m = 400m \\ (s - a) = 200m \\ (s - b) = 160m \\ (s - c) = 40m \\$

Area of /\ ABC,

$= \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{400 \times 200 \times 160 \times 40} {m}^{2} \\ = ( \frac{1600 \times 1.41}{10000} )hectares \\ = 2.26hectares.$

For /\ ACD, we have

$a = 240m \: b = 320 \: and \: c = 400m$

$s = \frac{1}{2} (240 + 320 + 400)m = 480m \\( s - a) = 240m \\ (s - b) = 160m \\ (s - c) = 80m$

Area of /\ ACD,

$\sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{480 \times 240 \times 160 \times 80} {m}^{2} \\ = (240 \times 160) {m}^{2} \\ = \frac{38400}{10000} hectares. \\ = 3.84 \: hectares$

Now /\ ACE and DCE have equal bases and the same height.

So, they are equal in area.

•°•area of /\ ACE = area of /\ DCE

$= \frac{3.84}{2} hectares \\ = 1.92 \: hectares$

Hence the area for wheat is 2.26 hectares while the area for each one of the potatoes and onions is 1.92 hectares.

${\huge{\mathtt{\red{Thank\:You}}}}$

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