The length of a rectangle is 7 more than the width. The area is 744 sqaure yards, find the length and width of the rectangle

Answer: Length of rectangle is 31 yards and Width is 24 yards. Given: The length of a rectangle is 7 more than the width. The area is 744 sqaure yardsSolution: Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.Using formula[tex] \\ \: \: \: \: \pink{ \dashrightarrow \: \: \: \: \sf { \underbrace{Area_{(Rectangle)} = Length × Width }}} \\ \\ [/tex]On Substituting the required values, we get;[tex]\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x = 24 \: or \: - 31 \\ \\ [/tex]As we know that width of the rectangle can't be negative. So x = 24 Hence, Width of rectangle = x = 24 yardsLength of the rectangle = x + 7 = 31 yards [tex] \therefore[/tex]Length of rectangle is 31 yards and Width is 24 yards.