The diagram shows a quadrilateral.The lengths of the sides of the quadrilateral are written as expressions.a Work out the lengths of the sides of the quadrilateral when a=−5 and b=2.b Use your answers to part a to work out the perimeter of the quadrilate when a=−5 and b=2.c Write an expression for the perimeter of the quadrilateral. Show that the expression can be simplified to a+4a2+19b.
Q. The diagram shows a quadrilateral.The lengths of the sides of the quadrilateral are written as expressions.a Work out the lengths of the sides of the quadrilateral when a=−5 and b=2.b Use your answers to part a to work out the perimeter of the quadrilate when a=−5 and b=2.c Write an expression for the perimeter of the quadrilateral. Show that the expression can be simplified to a+4a2+19b.
Calculate Side Lengths: Calculate the side lengths of the quadrilateral using the given values a=−5 and b=2. Let's assume the expressions for the sides are: Side 1 = a+3 Side 2 = 2a−b Side 3 = 4b+1 Side 4 = a2−2b+7
Plugging in the values: Side 1 = −5+3=−2 Side 2 = 2(−5)−2=−12 Side 3 = 4(2)+1=9 Side 4 = (−5)2−2(2)+7=25−4+7=28
Calculate Perimeter: Calculate the perimeter of the quadrilateral using the side lengths from Step 1.Perimeter = Side 1+Side 2+Side 3+Side 4Perimeter = −2+(−12)+9+28=23
Write Perimeter Expression: Write an expression for the perimeter of the quadrilateral and simplify it.Expression for perimeter = (a+3)+(2a−b)+(4b+1)+(a2−2b+7)Combine like terms:=a+2a+a2+3−b+4b−2b+1+7=a2+3a+b+11Simplified expression: a2+3a+b+11
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