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.

AgentFatboy
Apr 10, 2018

#1**+2 **

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 !!!

CPhill
Apr 10, 2018