Question

The length of a tarpaulin is 3ft. more than thrice its width and its area is 126ft². What is the length of the tarpaulin?​

Answer 1

Length = 22 ft

Width = 6 ft

Explanation:

Let the width of the tarpaulin be x meters.

Therefore, length = 3x + 3

Area of tarpaulin = 126 ft²

`x(3x + 3) = 126 \\ \\ 3x(x + 1) = 126 \\ \\ {x}^(2) + x = (126)/(3) \\ \\ {x}^(2) + x = 42 \\ \\ {x}^(2) + x - 42 = 0 \\ \\ {x}^(2) + 7x - 6x - 42 = 0 \\ \\ x(x + 7) - 6( {x + 7)} = 0 \\ \\ (x + 7)(x - 6) = 0 \\ \\ x + 7 = 0 \: \: or \: \: x - 6 = 0 \\ \\ x = - 7 \: \: or \: \: x = 6 \\ \\ \because \: x \: is \: side \: length \\ \therefore \: it \: can \: not \: be \: negative \\ \implies \: x \\otin - 7 \\ \\ \implies \: x = 6 \\ \\ 3x + 3 = 3 * 6 + 3 \\ \\ 3x + 3 = 18 + 3 \\ \\ 3x + 3 = 21 \\ \\ length \: of \:the \: tarpaulin \: = 21 \: ft \\ \\ width \: of \: the\: tarpaulin \: = 6 \: ft \\`