Posted by **Christine** on Sunday, June 7, 2009 at 5:12pm.

A) A rectangle has perimeter 64 cm and area 23 cm^2. Solve the following system of equations to find the rectangle's dimensions.

length=23/width

length + width = 32

B) Solve the system of equations

x^2+y^2=1

xy=0.5

- Math -
**MathMate**, Monday, June 8, 2009 at 8:59am
A) A rectangle has perimeter 64 cm and area 23 cm^2. Solve the following system of equations to find the rectangle's dimensions.

length=23/width

length + width = 32

Let

L = length

W = width

L=23/W

L+W=32

23/W+W=32

W^{2}-32W+23=0

Solve for the quadraticequation in W.

Find L using L = 23/W.

You should get 0.7 and 31 approx.

B. Solve

x^2+y^2=1

xy=0.5

If you plot the two equations on sqaure paper, you will see a circle (firt equation) and two disjoint curves with asymptotes toward the 4 extremities of the axes. This will give you an idea where the roots will be, namely where they intersect, and that there should be four of them if they cut the circle, zero if they don't, and two (visually) if they are tangential to the circle.

Substitute y=0.5/x into the equation of the circle (with unit radius).

x^{2} + (0.5/x)^{2} = 1

substitute u=x^{2},

u+0.25/u=1

u^{2} -u + 0.25 = 0

Solving for u, we get

u=0.5 ħ 0 (meaning the intersection is tangential)

=0.5

x=ħsqrt(0.5)

y=0.5/x=ħsqrt(0.5)

## Answer this Question

## Related Questions

- algebra , help - Can someone help me set up the equations thanks. Directions: ...
- Math - The perimeter of a rectangle is 42ft. The length is 7ft. longer than the ...
- MAT 116 - The perimeter of a rectangle is 28 ft. The length is 10 ft longer than...
- math - Solve each system of equations by graphing. Check each solution. The ...
- algebra - the primeter of a rectangle is 24ft. the length is 2 ft longer than ...
- algebra - the primeter of a rectangle is 24ft. the length is 2 ft longer than ...
- math 209 - The perimeter of a rectangle is 44ft the length is 4ft longer than ...
- math ,correction - Directions: Solve each of the following problems. Be sure to ...
- algebra - Solve system of equations to model the problem then solve: The length...
- algebra - Solve system of equations to model the problem then solve: The length...