Question

AREA AND VOLUMEInvestigating the effects on the area for non-proportiona

Answer 1

(a)

Let:

w1 = Original width

l1 = Original length

w2 = New width

l2 = New length

A1 = Original area

A2 = New Area

so:

`\begin{gathered} w2=3w1=3\cdot10=30ft \\ l2=2l1=2\cdot50=100ft \\ A2=w2\cdot l2=3000ft^2 \end{gathered}`

Answer:

New length: 100ft

New width: 30 ft

New Area: 3000ft²

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(b)

`(A2)/(A1)=(3000)/(500)=6`

Answer:

The area of the new walkway will be 6 times the area of the current walkway

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(c)

`\begin{gathered} 8\cdot500=x\cdot50\cdot4\cdot10 \\ 4000=2000x \end{gathered}`

Solve for x:

`\begin{gathered} x=(4000)/(2000) \\ x=2 \end{gathered}`

Answer:

Make the new length 2 times the current length.