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jarptica [38.1K]
3 years ago
11

A rectangle has an area of 48 in^2. Every dimension of the rectangleis multiplied by a scale factor, and the new rectangle has a

n area of 12 in^2. What is the scale factor?
Mathematics
1 answer:
jeka57 [31]3 years ago
5 0

Let the dimensions of the first rectangle be L and W.  Then L*W = 48 in^2.

If we multiply both dimensions of this first rectangle by scale factor f, we get

f*L * f^W = 12 in^2.  Our job is to determine the scale factor, f.

Note that f^2*L*W = 12 in^2, and that LW = 48 in^2.

Therefore, the above equation becomes f^2*(48 in^2) = 12 in^2.

Dividing both sides by (48 in^2), we get f^2 = 1/4.

Solving for the scale factor, we get f = √(1/4) = 1/2.

The scale factor is 1/2.

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Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent.  Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.

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