Finding lengths using scale factor
Question
Shape \(WXYZ\) is an enlargement of shape \(wxyz\). What is the length of \(XY\)?
XY is on the bigger figure, therefore we will be using an enlargement scale factor.
\(SF_{Enlargement} = \frac{Big}{Small} = \frac{9}{8}\)
Therefore \(XY\) is \(\frac{9}{8}\)times \(xy\).
So, \(XY = \frac{9}{8} \times 4 = 4.5cm\)
Question
Shape \(WXYZ\) is an enlargement of shape \(wxyz\). What is the size of angle \(WXY\)?
In an enlargement or reduction of a shape the angles stay the same. So angle \(WXY\) is \(57^{\circ}\).
Question
The sides of a rectangle measure \(8cm\) and \(6cm\).
If the rectangle is to be enlarged using scale factor \(\frac{3}{2}\) what will be the new lengths of the sides?
\(\frac{3}{2}\times 8 = 12cm\)
\(\frac{3}{2}\times 6 = 9cm\)
The new lengths will be \(12cm\) and \(9cm.\)
Question
The sides of a rectangle measure \(20\,cm\) and \(28\,cm\).
If the rectangle is to be reduced using scale factor \(\frac{3}{4}\) what will be the new lengths of the sides?
\(\frac{3}{4}\times 20 = 15cm\)
\(\frac{3}{4}\times 28 = 21cm\)
The new lengths will be \(15cm\) and \(21cm\).
