Answer:
[tex]H = 59.4[/tex]
Step-by-step explanation:
The question is an illustration of dilation.
From the small shape, we have:
[tex]Body = 3[/tex]
[tex]Height = 2.2[/tex]
From the big shape, we have:
[tex]Body = 81[/tex]
Height = ??
Because it is a dilation, the ratio of the bodies must be equal to the ratio of the heights
i.e.
[tex]Body_{Small} : Body_{Big} = Height_{Small} : Height_{Big}[/tex]
Substitute the right values
[tex]3 : 81 = 2.2 : H[/tex]
Express as fraction
[tex]\frac{3}{81} = \frac{2.2}{H}[/tex]
[tex]\frac{1}{27} = \frac{2.2}{H}[/tex]
Make H the subject
[tex]H = 2.2 * 27[/tex]
[tex]H = 59.4[/tex]
Hence, the height of the big shape is 59.4 units
