Question

The cost of turfing a triangular field at 45 per 10 m² is ₹900. Find its altitude if the base is four times the altitude.​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

→ in Rs.45 the farmer can turf area of = 100m²

→ in Rs.1 the farmer can turf area of = (100/45)m²

→ in Rs.900 the farmer can turf area of = (100/45) * 900 = 2000m².

Therefore, area of triangular field is 2000m².

Now, Let us Assume that, Base of the triangular field is B m and Height of triangular field is H m.

Than ,

→ Area of triangular field = (1/2) * B * H

So,

→ (1/2) * B * H = 2000 m²

→ B * H = 4000m² -------------- Eqn(1)

Now, we have given that,

→ Double the base of ∆ = 5 Times the height .

→ 2B = 5H

→ B = (5H/2) ------------------ Eqn(2)

Putting value of Eqn.(2) in Eqn.(1) Now,

→ (5H/2) * H = 4000

→ 5H² = 4000 * 2

→ H² = 800 * 2

→ H² = 400 * 2 * 2

→ H² = (20)² * (2)²

→ H = 20 * 2

→ H = 40m. (Option D) (Ans.)

Putting this value in Eqn.(2) Now,

→ B = (5 * 40)/2

→ B = 5 * 20

→ B = 100m. (Option A) (Ans.)

Hence, Base of triangular field is 100m & Height of triangular field is 40m.

Note : - since Area is given in m² , Base and height will also in m. (in Option it is given cm, which is misprint.)

Answer 2

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