A rectangle has a perimeter if 46 cm and an area of 120 cm^2. How do you find its dimensions by writing an equation and using the quadratic formula to solve it?

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Answer 1 · 2018-04-07T13:18:52

The dimensions are 8 cm and 15 cm.

Let the length be #x# and the width be #y#

The perimeter of the rectangle is #2x+2y#

The area of the rectangle is #xy#

We now have two equations,

#2x+2y=46 or x+y=23# we’ll call this equation (1)

And #xy=120# equation (2)

From (2), #y=120/x#, substitute this into (1)

#therefore x+120/x=23#

#x^2+120=23x# multiply both sides by #x#

#x^2-23x+120=0# subtract #23x# from both sides

#(x-8)(x-15)=0# factorise

#x=8 or 15# solve linear equations

From (2), when #x=8, 8y=120=>y=15#

When #x=15, 15y=120=>y=8#

#therefore# the dimensions are #8# cm and #15# cm.