<span>Let the width of the rectangular plot of land be 'x' yards. Given that the length of the rectangular plot of land is 10 yards more than its width. So, width of the rectangular plot of land = (x + 10) yards. Also given that the area of the rectangular plot of land is 600 square yards. We know that, area of a rectangle = length * width That is, (x+10) * x = 600 x^2 + 10x = 600 x^2 + 10x - 600 = 0 x^2 + 30x - 20x -600 = 0 x(x + 30) - 20(x + 30) = 0 (x +30)(x -20) =0 Therefore, either (x + 30) = 0 or (x - 20) = 0 If x + 30 = 0, then x = -30 and If x - 20 = 0, then x = 20 Since 'x' represents the width of a rectangular plot of land it cannot be negative. Therefore, width of the rectangular plot of land = 20 yards length of the rectangular plot of land= x + 10 = 30 yards</span>

5 0

4 years ago

What is the length of the rectangle?

gregori [183]

Step-by-step explanation:

$area \: of \: rectangle \: = 60 \: {yards}^{2} \\ \therefore \: (w + 4) \times \: w = 60\\ \\ \therefore \: {w}^{2} + 4w -60 = 0 \\ \\ \therefore \: {w}^{2} + 10w - 6w -60 = 0 \\ \\ \therefore \: w({w} + 10) - 6(w + 10)= 0 \\ \\ \therefore \: ({w} + 10) (w- 6)= 0 \\ \therefore \: {w} + 10 = 0 \: or \: w- 6 = 0 \\ \therefore \: {w} = - 10 \: or \: w = 6 \\ \because \: sides \: of \: rectangle \: cant \: be \: negative \\ \therefore \: w \neq \: - 10 \\ \\ \therefore \: w = 6 \\ \\ \therefore \: w + 4 = 6 + 4 = 10 \\ \\ length \: of \: rectangle \: = 10 \: yards.$

4 0

3 years ago