Given that in rectangle ABCD the longest sides are DC and AB and in the rectangle RSTU the longest sides are UT and RS ⇒ The scale factor of a dilation will transform the sides DC and AB into UT and RS

Working with the lengths of the sides :

DC.(Scale factor) = UT

AB.(Scale factor) = RS

Replacing with the values of the lengths (Scale factor : SF) :

$DC.SF=UT\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}$

$AB.SF=RS\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}$

Notice that the scale factor is dimensionless.

We can verify this result with the sides AD and BC :

$AD.SF=UR\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft$

$BC.SF=TS\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft$

The scale factor (SF) is $\frac{1}{2}$

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What is the surface area of a cube in which each face of the cube has an area of 7 cm2? surface area = a0 cm2?

inessss [21]

The cube has 6 this same faces.
Therefore the surface area is equal 6 · 7cm² = 42cm²

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