Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

The area of a rectangle is 12 square inches. The length is 5 more than twice the width. Find the length and width

Sagot :

CamilleEaton210
Since the equation for area of a rectangle is A = l×w, and the length is 5 more than twice the width, making it 2w + 5, you have to plug in the quantities.
A = l×w
12 = (2w+5)×w
12 = 2w²+5w
0 = 2w²+5w-12
0 = (2w-3)(w+4)
Since the width can't be a negative number, the answer is:
2w-3 = 0
2w = 3
w = 3/2
And now, since length is 2w+5, you plug in the value of the width into the equation.
2(3/2)+5
3+5
8
olemakpadu
Let the width of the triangle be x.
Therefore length  = 2x + 5.         (5 more than twice its width).

Area =  L * W =  (2x + 5) x = 12.
                         2x^2 + 5x = 12
                         2x^2 + 5x - 12 = 0.
This is a quadratic equation.  (2)*(-12) = -24.
We think of two numbers whose product is -24 and it sum is +5.
Those two numbers are 8 and -3. So we replace the middle term of
quadratic with  (8 -3).
                         2x^2 + 5x - 12 = 0.
                         2x^2 + 8x-3x - 12 = 0.  Factorize.
                         2x(x + 4) - 3(x +4) = 0
                          (2x-3)(x+4)  = 0.
(2x-3)  = 0    or    (x+4)  = 0
2x = 3.                x = 0 -4
x = 3/2 = 1.5        x = -4.     (x can't be negative, since we are solving for lengths)
x = 1.5 is only valid solution.

width = x = 1.5
Length = (2x + 5) = 2*1.5 +5 = 3 + 5 =8.
Therefore length = 8, and width = 1.5   
Cheers.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.