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# last one

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2 If the area of rABC is 20 cm2, what is the area of rPQR?

If you can please show how you got your answer, I'm a bit confused on this question.

Apr 10, 2018

### 2+0 Answers

#1
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The scale factor  from   ABC  to RQR  is      6/4  =  3/2  =  1.5

So....each dimension  of  PQR  is 1.5 times that of ABC

Now....just for the heck of it,if we let the base of ABC  = 4 cm...so.... its altitude must be 10 cm

Proof  ..area ABC  =   (1/2) base * altitude  =  (1/2) (4) (10)  =  20  cm^2

So....since each dimension of PQR  is 1.5 times that of ABC, its altitude must be 10 * 1.5  = 15 cm

And let its base  = 6cm

So...it's area is just  (1/2) (6) ( 15)  =  45 cm^2

Note that  we could obtain the same result  by taking the area of ABC  and multiplyng this by the square of the scale factor

Proof :   20 (1.5)^2   =  20 (3/2)^2  =  20 * 9 / 4  =  180  / 4   = 45  cm^2

Hope that helps  !!!   Apr 10, 2018
#2
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yup that helps, thank ya

AgentFatboy  Apr 10, 2018