The Phillips family members wants come fence their backyard. They recognize the yard has a perimeter that 24 meters and an area of 32 square meters. What is the yard"s length and width?Assuming that the yard is a rectangleArea = size × width32 = length × widthPerimeter = 2 × size + 2 × width24 = 2 × size + 2 × widthUsing 32 = size × width, broad = 32 / lengthReplace width = 32 / length in 24 = 2 × length + 2 × widthWe get:24 = 2 × size + 2 × (32 / length)24 = 2length + 64 / length24 - 2length = 64 / lengthMultiply both political parties by length24 × length - 2length × length = ( 64 × length ) / length24length - 2length2 = 6424length - 24length - 2length2 = 64 - 24length 0 - 2length2 = + 64 - 24length 0 - 2length2 + 2length2 = 64 - 24length + 2length20 + 0 + = 64 - 24length + 2length22length2 - 24length + 64 = 0Divide both political parties by 2length2 - 12length + 32 = 0Look for factors of 32 that will include up to -12-8 × -4 = 32 and also -8 + -4 = -12So our determinants are -8 and -4We get (length + -8) × (length + -4) = 0length + -8 = 0length + -4 = 0length = 8length = 4If size = 8, broad = 32 / size = 32 / 8 = 4If size = 4, broad = 32 / length = 32 / 4 = 8Thus, one of two people the size = 4 and also the width = 8 or the length = 8 and also the broad = 4
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