Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.