Question

The length of the top of a table is 4 m greater than the width. The area is 60m^2. Find the dimensions of the table

Answer 1

Width = 6 m

Length = 10 m

Explanation:

Let the width of the table be x meters.

Therefore, length of the table = (x + 4) meters.

`length * width = Area \\ \\ x(x + 4) = 60 \\ \\ {x}^(2) + 4x - 60 = 0 \\ \\ {x}^(2) + 10x - 6x - 60 = 0 \\ \\ x(x + 10) - 6(x + 10) = 0 \\ \\ (x + 10)(x - 6) = 0 \\ \\ x + 10 = 0 \: \: or \: \: x - 6 = 0 \\ \\ x = - 10 \: \: or \: \: x = 6 \\ \\ \because \: dimensions \: can \: not \: be \: negative \\ \therefore \: x \\otin \: 10 \\ \implies \: x = 6 \\ x + 4 = 6 + 4 = 10 \\ width \: of \: table = 6 \: m \\ length \: of \: table = 10 \: m`