the cost of a turfing field at the raye of 45 rupees per 100m2 is 900 rupees .If double the base of triangle is 5 times the height .then,answer the above questions
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The cost of turfing a triangular field at the rate of Rs. 5 per sq.m is Rs. 1350 .If the sides of the field are in the ratio of 5:12:13. Find the sides of field .
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Answers
Given :-
Cost of turfing a triangular field @ Rupees 5 per m² is rupees 1350.
Therefore area of the triangular field = 1350/5
= 270m²
Now,
Ratio between the sides of the triangular field is given 5 : 12 : 13
Let the sides of the triangular field be 5x, 12x and 13x respectively.
➡ Semi-perimeter of the triangle = (5x + 12x + 13x)/2
= 15x
By using heron's formula, we get
√s(s - a)(s - b)(s - c) = area of the triangle where s is the semi-perimeter and a, b and c are it's sides respectively.
➡ √[15x(15x - 5x)(15x - 12x)(15x - 13x)] = 270m²
➡ √(15x × 10x × 3x × 2x) = 270m²
➡ √(900x⁴) = 270m²
➡ 30x² = 270m²
➡ x² = 270/30
➡ x² = 9
➡ x = √9
➡ x = 3
Hence, the sides of the triangular field are :-
5x = 5 × 3 = 15m
12x = 12 × 3 = 36m
13x = 13 × 3 = 39m
Answer:
Area of the triangular field
=
45
100
×900m
2
=2000m
2
Let base of the triangular field be x and height of the field be y
Given, 2x=5y
∴x=
2
5y
Now,
Area of the triangular field =
2
1
× base × height
⟹2000=
2
1
×x×y
⟹4000=
2
5y
×y
⟹y
2
=1600
⟹y=40m