SOLUTION: Please explain and solve. Thank you.
A rain gutter is made from sheets of aluminum that are 20 inches wide. Determine the depth of the gutter that will allow a cross-sectional are
Algebra.Com
Question 263025: Please explain and solve. Thank you.
A rain gutter is made from sheets of aluminum that are 20 inches wide. Determine the depth of the gutter that will allow a cross-sectional area of 13 square inches. Show that there are 2 different solutions to the problem. Round to the nearest tenth of an inch.
x(20+2x)= 13.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A rain gutter is made from sheets of aluminum that are 20 inches wide. Determine the depth of the gutter that will allow a cross-sectional area of 13 square inches. Show that there are 2 different solutions to the problem. Round to the nearest tenth of an inch.
x(20+2x)= 13.
----------------------
The cross-section is a slice thru the gutter from top thru the bottom.
The shape is a "U".
----
If height = base = x inches you get x^2 = 13 and x = sqrt(13)
--------------------------------------------
If base is x then height is (20-x)/2:
x(20-x)/2 = 13
20x - x^2 = 26
x^2 -20x + 26 = 0
x = [20 +- sqrt(400 - 4*1*26)]/2
x = [20 +- sqrt(296)]/2
x = [20 + 17.2]/2 = 37.2/2 = 18.6"
OR
x = [20 - 17.2]/2 = 1.4"
---
So base could be 18.6 and height be (1.4/2) = 0.7"
Or base could be 1.4" and height be (18.6/2) = 9.3"
====================================================
Cheers,
Stan H.
RELATED QUESTIONS
A rain gutter is made from sheets of aluminum that are 20 inches wide. The edges are... (answered by ankor@dixie-net.com)
A rain gutter is made from sheets of aluminum that are
12 inches wide by turning up... (answered by stanbon)
A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the... (answered by ankor@dixie-net.com)
A rain gutter is made from sheets of aluminum that are 19 inches wide. The edges are... (answered by htmentor)
Draw and label a diagram for problem 1.Write answers as complete sentences
1. A rain... (answered by solver91311)
a rain gutter is made from sheets of aluminum that are 28 inches wide. The edges are... (answered by KMST)
a rain gutter is made from sheets of aluminum that are 27 inches wide. The edges are... (answered by ankor@dixie-net.com)
A rain gutter is to be made of aluminum sheets that are 36 inches wide by turning up the... (answered by greenestamps)
A rain gutter is made from sheets of aluminum that are 17 inches wide. As shown in... (answered by ankor@dixie-net.com)