Question 1027866
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If the perimeter of a rectangle is 46 cm and the area is 120 square cm, then what are the dimensions of the rectangle? 
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Let x be the length and y be the width.

Then 

x + y =  23,   (1)     ( 23 = {{{46/2}}} )
xy    = 120.   (2)

Express x = 23 - y from (1) and substitute into (2). You will get

(23-y)*y = 120.

Solve this quadratic equation:

{{{23y - y^2}}} = {{{120}}},

{{{y^2 - 23y + 120}}} = {{{0}}}.

Factor the left side:

(x - 15)*(x-8) = 0.

The roots are 8 and 15.

The width, or shorter side is   8 cm.
The length, or longer side is  15 cm.
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