Question

Someone help ASAP!!!!!!

Answer 1

Answer:

Length, l = 11 ft.

Width, w = 9 ft.

Step-by-step explanation:

From the given data, the area of the rectangle = 99 ft².

Area of the rectangle = Length, l X Width, w

Here, Length, l = 7 more than twice the width

⇒       Length, l = 7 + 2w

Therefore, Area, A = 99 = (7 + 2w)w

⇒ 99 = 7w + 2w²

⇒ 2w² + 7w - 99 = 0

Solve the Quadratic equation using the formula: x = $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for the quadratic equation ax² + bx + c = 0.

Therefore, w = $\frac{-7 \pm \sqrt{7^2 -4(2)(-99)}}{2(2)}$

$= \frac{-7 \pm \sqrt{49 + 8(99)}}{4}$

$= \frac{-7 \pm + \sqrt{841}}{4}$

Since, $\sqrt{841} = 29$ we get:

$w = \frac{-7 \pm 29}{4}$

This gives two values of 'w', viz., w = $\frac{-7 - 29}{4}$, $\frac{-7 + 29}{4}$

$\implies w = \frac{22}{4}, \frac{-36}{4}$

⇒ w = $\frac{22}{4}$, -9.

We take the integer values.

If w = -9, then l = 2(-9) + 7

⇒ l = - 18 + 7 = - 11

Therefore, the length, l of the rectangle = - 11 ft.

and the width, w of the rectangle = - 9 ft.

Hence, the answer.