Answer:
12 cm by 14 cm
Step-by-step explanation:
The area is given by ...
A = LW
The perimeter is given by ...
P = 2(L +W)
Substituting the given values, we have ...
168 = LW
52 = 2(L +W)
The second equation can be used to find an expression for L:
26 = L +W . . . . . divide by 2
L = 26 -W . . . . . subtract W
Using this in the first equation, we have ...
168 = (26 -W)(W)
W² -26W +168 = 0
Factors of 168 are ...
168 = (-1)(-168) = (-2)(-84) = (-3)(-56) = (-4)(-42) = (-6)(-28) = (-7)(-24)
= (-8)(-21) = (-12)(-14)
Only the last factor pair (-12, -14) has a sum of -26, so the equation factors as ...
(W -12)(W -14) = 0
Solutions are W=12, and W=14. The corresponding values of L are 14 and 12.
The quadrilateral has dimensions of 12 cm and 14 cm.
