Question

Sita ram has agriculture land in the form of given shapes. He want to distribute equally his land

among his two son Ramesh and Ram . Ramesh has got 1

st

triangular land . Ram has got 2nd

triangular land.

(i) Ramesh got how much land?

(ii) Ram got how much land?

(iii) Who got less land ? how much land he will occupy more from rectangular field then they will get

equal land?​

Answer 1

Given :- Sita ram has agricultural land in the form of given shapes. He want to distribute equally his land among his two son Ramesh and Ram. Ramesh has got 1" triangular land. Ram has got 2 triangular land.

(1) Ramesh got how much land ?

(2) Ram got how much land ?

(3) Who got less land ?

(4) How much land he will occupy more from rectangular field then they will get equal land ?

Solution :-

Ramesh :- First Triangular Land.

• Sides of triangular land are 13m, 14m and 15m.

we know that,

• Area of ∆ with sides as a, b , c and semi - perimeter as s is = √[s * (s - a) * (s - b) * (s - c)]

So,

→ s = (13 + 14 + 15)/2 = 21m.

Than,

→ Area of first triangular land = √[21 * (21 - 13) * (21 - 14) * (21 - 15)] = √[(7*3) * (2*2*2) * (7) * (2*3)] = √[(7)² * (4)² * (3)²] = 7 * 4 * 3 = 84 m².

Hence, Ramesh got 84m² land . (Answer 1).

Ram :- second Triangular Land.

• Right angled triangle with Base 5 and perpendicular height at 12m.

we know that,

• Area of right angled ∆ is = (1/2) * Base * perpendicular height .

So,

→ Area of second triangular land = (1/2) * 12 * 5 = (1/2) * 60 = 30m².

Hence, Ram got 84m² land . (Answer 2).

Now,

→ 84 m² > 30m².

→ First Triangular Land > Second Triangular Land.

→ Ramesh > Ram.

Hence, Ram got less Land. (Answer 3).

Now,

→ Total agriculture land sita ram has = first triangular field + second triangular field + rectangular field. = 84 + 30 + 160 = 274 m².

As, he want to distribute equally among his sons .

So,

→ Ram and Ramesh gets = 274/2 = 137m².

Now,

→ Ram already has land(2nd ∆) = 30m².

So,

→ He gets land from rectangular field = 137 - 30 = 107m² of rectangular land.

and,

→ Ramesh has land(1nd ∆) = 84m².

→ He gets land from rectangular field = 137 - 84 = 53m² of land.

Therefore,

→ Ram occupy more land from rectangular field by = 107 - 53 = 54m².

Hence, Ram occupy 54m² more land from rectangular field when they gets equal land . (Answer 4).

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