Question 272992
Write the equation for each statement
:
A rect. has a perimeter of 68 cm,
2L + 2W = 68
Simplify, divide by 2
L + W = 34
or
L = (34-W); use this form for substitution
:
it's area is 273 sq.cm.
L * W = 273
Substitute (34-W) for L
(34-W)*W = 273
-W^2 + 34W = 273
Arrange as a quadratic equation
-W^2 + 34W - 273 = 0
multiply by -1, it's easier to factor
W^2 - 34W + 273
Factors to
(W -  13)(W - 21) = 0
Two solutions
W = 13
and
W = 21
:
W = 13 is the width and L = 21 is the length
;
:
You can check this by finding the perimeter and area with these values.