Question

A rectangular garden has an area of 24 square meters. The width is 8 meters less than twice the length. Find the dimensions of the garden
The garden is
meters long by
meters wide.

Answer 1

Answer:

Length: 6 m

Width: 4 m

Step-by-step explanation:

Area: 24 $m^{2}$

Width: 2L - 8 m

Length: ?

Formula: A = W * L

Replace the variables:

24 = (2L - 8) * L

24 = 2$L^{2}$ - 8L

0 = 2$L^{2}$ - 8L - 24

or

2$L^{2}$ - 8L - 24 = 0

Solve; if you don't know how to solve it using this method, let me know. It's the expression $Ax^{2} +Bx+C$

1. $2 (\frac{(2L^2 - 8L - 24)}{2})$

2. $\frac{(2L)^2 - 8(2L) - 48}{2}$

3. $\frac{(2L - 12)(2L + 4)}{2}$

4. $2(\frac{(L - 6)(2L + 4)}{2})$

5. (L-6) (2L+4)

6. L-6 = 0 AND 2L+4 = 0

L - 6 =0

L = 6

---------------------------------

2L = -4

L = $\frac{-4}{2}$

L = -2

Since the length cannot be negative, the only real value is 6.

Area: 24 $m^{2}$

Width: 2L - 8 m

Length: 6 m

Calculate width:

W = 2L - 8

W = 2(6) - 8

W = 12 - 8

W = 4 m