The perimeter of a square field is 18 cm more than the perimeter of a rectangle. The length of the rectangle is 77 cm which is 350% of its width. If a street of width 10 cm surrounds from outside the square, then find the total cost of constructing the street at the rate of Rs. 26 per sq. cm?
Let the width of the rectangle = x cm Then, 350% of x = 77 x = 77 × 100/350 = 22 cm Perimeter of the rectangle = 2(length + width) = 2 × (77 + 22) = 198 cm Perimeter of the square = (198 + 18) = 216 cm The sides of the square = 216/4 = 54 cm The area of the square field without street = (54)2 sq. cm = 2916 sq. cm The area of the square field with street = (54 + 20)2 sq. cm = 5476 sq. cm The area of the street = 5476 – 2916 = 2560 sq. cm The total cost of constructing the street = 2560 × 26 = Rs. 66,560
If sinA = 3/5 and cosB = 12/13, where A and B are in the first quadrant, find sin(A + B).
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