Question

The areas of two similar triangles are 80 square feet and 500 square feet.

What scale factor applied to the smaller rectangle will give the larger triangle?

A. 25/64

B. 25/4

C. 5/8

D. 5/2

Answer 1

So in order to get the small rectangle big we need a whole number bigger that 1 or an improper fraction so let's cross out the answer choices that don't meet the above requirements!!

A and C are not improper fractions and are less than 1 so they're wrong!!

We can solve by making an equation,


`80x = 500`

So 80 × what will give us 500.

We can do this two ways and I'll show you both!!


`(80x)/(80) = (500)/(80)`

We can divide both sides by 80 and get,


`x = (25)/(4) = 6.25`

Which is answer choice B which makes sense since answer choice D is too small.

Or, we can plug in our two answer choices and see if it checks out to be 500!!


`80( (25)/(4) ) = 500`

The above statement is true!!


`80( (5)/(2) ) = 500`

The above statement is false since 80 × 5/2 = 200, not 500, the number we need!!