Question

What is the side of that equilateral triangle whose area costs as much to pave at Rs. 10 per square metre as it would cost to fence the three sides at Rs. 25 a metre ?
(1) 17.32 m
(2) 16.35 m
(3) 18.32 m
(4) 19.32 m

Answer 1

Answer:

Option (1) : 17.32 m

Step-by-step explanation:

Let the side be x m

Find the area of the triangle in term of x:

Area of a equilateral triangle = √3/4 side²

Area of the equilateral triangle = √3/4 (x)²

Find the cost of the pave:

1 m² = Rs 10

√√3/4 (x)²  = 10(√3/4 x²)

√√3/4 (x)²  = 10(√3/4)(x)²

√√3/4 (x)²  = 5(√3/2) (x)²

Find the perimeter:

Perimeter = side 1 + side 2 + side 3

Perimeter = x + x + x = 3x

Find the cost of the fencing:

1 m = Rs 25

3x m = 25(3x)

3x m = Rs 75x

Solve x:

Given that the cost is the same

5(√3/2) (x)²  = 75x

5√3 (x)² = 150x

5√3 (x)² - 150x = 0

√3 (x)² - 30x = 0

x (√3 (x) - 30) = 0

√3 (x) = 30 or x = 0 (rejected, since length cannot be zero)

x = 30 ÷ √3

x = 17.32 m

Answer: (1) 17.32 m