You are planning to close off the corner of the first quadrant with a line segment 20 units long running from (a,0) to (0,b). Show that the area of the triangle enclosed by the segment is largest when a=b

From applications of derivatives...this is really tough!!

Write the equation that relates a to b:
a^2 + b^2 = 20^2 = 400
Now differentiate with respect to a, with b as a function of a.
2 a + 2 b db/da = 0
db/da = -(a/b)

Area = a b/2
Call the area A
dA/da = 0 at maximum
b + a db/da = 0
b + a (-a/b) = 0
a^2/b = ba^2 = b^2
Therefore a = b, since both are positive

1. 👍 0
2. 👎 1
3. 👁 736
1. a line through ( 0,13) is 5 units from the origin in quadrant 1. find the equation.

1. 👍 0
2. 👎 0
posted by Jane

## Similar Questions

1. ### calculus

You are planning to close off a corner of the first quadrant with a line segment 20 units long running from (a,0) to (0,b). Show that the area of the triangle enclosed by the segment is largest when a=b. Can anyone please give me

asked by Toby on December 3, 2008
2. ### calculus

Find the area of the largest rectangle with one corner at the origin, the opposite corner in the first quadrant on the graph of the line f(x)=20-5x , and sides parallel to the axes.

asked by ali on November 3, 2008
3. ### Geometry

Yes, I'm this desperate. I just have problems with coming up with the statements for two column proofs. Answers would be appreciated. Given: line segment AX congruent to line segment DX, line segment XB is congruent to XC. Prove:

asked by Derp on October 5, 2010
4. ### Algebra

A segment bisector is a line, ray, or segment that divides a line segment into two equal parts. In the triangle formed by points A(-1,7), B(1,2), and C(7,6), what is the slope of the line that goes through point A and bisects BC?

asked by Vaililly on July 24, 2019
5. ### Calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2+7 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent

asked by Lynnn on April 8, 2012

Quadrilateral WXYZ os describes below. Line segment WX is parallel to line segment YZ. Line segment XY is the same length as line segment ZW. Line segment Xy is not parallel to line segment ZW. Which of the following describes

asked by Grace on April 9, 2015
7. ### Geometry-8th gr

Find KN and LM. In triangle LKM, angle L is bisected. Line segment LK is 11, line segment KN is x-4, line segment NM is 5.4, and line segment LM is 2x + 1.3 (there is a drawing of this triangle) Thanks.

asked by Mona on February 1, 2013
8. ### Geometry

Find KN and LM. In triangle LKM, angle L is bisected. Line segment LK is 11, line segment KN is x-4, line segment NM is 5.4, and line segment LM is 2x + 1.3 (there is a drawing of this triangle) Thanks.

asked by Kaylee on February 1, 2013
9. ### math

Line segment segment CD has a slope of negative start fraction two over three end fraction and contains point C(−3, −6). What is the y-coordinate of point Q(−1, y) if segment QC is perpendicular to line segment segment CD

asked by Natalia on March 30, 2016
10. ### Complete the two-column proof

Complete the two-column proof Given: triangle SVX is congruent to triangle UTX and Line SV is || to line TU Prove: VUTS is a parallelogram Image: It's a parallelogram, with one line going from corner S to corner U and a line going

asked by Unknown on January 18, 2017

More Similar Questions