Question

Do y’all the answer?

Answer 1

Length = 12 m and width = $\frac{7}{2}$ m.

Solution:

Let the width of the rectangle be w.

Length of the rectangle = 2w + 5

Area of the rectangle given = 42 m²

Area of the rectangle = length × width

length × width = 42

(2w + 5) × w = 42

$2w^2+5w=42$

Subtract 42 from both sides, we get

$2w^2+5w-42=0$

Using quadratic formula,

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here, $a=2, b=5, c=-42$

$w=\frac{-5 \pm \sqrt{5^{2}-4 \cdot 2(-42)}}{2 \cdot 2}$

$w=\frac{-5 \pm \sqrt{25+336}}{4}$

$w=\frac{-5 \pm \sqrt{361}}{4}$

$w=\frac{-5 \pm19}{4}$

$w=\frac{-5+19}{4}, w=\frac{-5-19}{4}$

$w=\frac{14}{4}, w=\frac{-24}{4}$

$w=\frac{7}{2}, w=-6$

Dimension cannot be in negative, so neglect w = –6.

Width of the rectangle = $\frac{7}{2}$ m

$L=2(\frac{7}{2} )+5=12 \ m$

Hence length = 12 m and width = $\frac{7}{2}$ m.