Question

The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rectangle.

Answer 1

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 $m^{2}$

From there

x * (2x - 4) = 70

$2x^{2}$ - 4x = 70

$2x^{2}$ - 4x - 70 = 0

$x^{2}$ - 2x - 35 = 0

Now we have a quadratic equation, which is  a$x^{2}$ + bx + c = 0, where a $\neq$ 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = $-2^{2}$  - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are  $\frac{- b - \sqrt{D} }{2a}$ and $\frac{- b + \sqrt{D} }{2a}$

$x_{1}$ =  $\frac{- (-2) - \sqrt{144} }{2}$ = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

$x_{2}$ = $\frac{- (-2) + \sqrt{144} }{2}$ = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)