The area of the of a rectangle is 336 square inches. if the perimeter is 76. what is the shorter sides length?

hello :

the perimeter is : p = 2 ( w + l )

The area is : A= w ×l       w : width       l : length       w ?

2 ( w + l )  = 76

w ×l  = 336

you have the system :

w + l = 38 ...(1)

w ×l  = 336...(2)

by (1) : l = 38 - w

subst in (2) : w ( 38 - w ) =336

38w - w²= 336

w² - 38w +336 = 0

delta = b² -4ac     when : a = 1   and  b= -38      c = 336

delta = (-38)² -4(1)(336) = 1444 - 1344  = 100 = 10²

w1 = (38-10)/2 = 14( the shorter sides length)

w2 = (38+10)/2 = 24( refused  )

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

step-by-step explanation:

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