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put this solution on YOUR website!Solve using a system of two equations and two unknowns.
A computer parts company wants to make a rectangular memory board that has
a perimeter of 28 centimeters and a diagonal length of 10 centimeters.
Find the dimensions of the board. Consider the length to be the longer side.
:
Call the two sides L & W
:
the perimeter
2L + 2W = 28
Simplify, divide by 2
L + W = 14
L = (14-W); use this form for substitution
:
The hypotenuse, (diagonal)
L^2 + W^2 = 10^2
L^2 + W^2 = 100
:
Replace L with (14-W)
(14-W)^2 + W^2 = 100
;
FOIL (14-W)*(14-W)
196 - 28W + W^2 + W^2 = 100
2W^2 - 28W + 196 - 100 = 0
:
A quadratic equation
2W^2 - 28W + 96 = 0
:
Simplify, divide by 2
W^2 - 14W + 48 = 0
:
Factors to
(W-6)(W-8) = 0
:
Two solutions
W = 6
and
W = 8
Make W = 6 cm as the width, then L = 8 cm as the length
:
:
Check our solution on a calc, find the hypotenuse:
Results: 10
