How do you find the perimeter by using just the scale factor?

Question

The diagonals of rhombus ABCD are 6ft and 8ft. Rhombus ABCD is dilated to rhombus RSTU with the scale factor 8. What is the perimeter of rhombus RSTU?

Answer 1

Hi Vivi,

 

The question above is "How to find the perimeter using just the scale factor?". The very simple answer to this question is multiply the scale factor to the perimeter of the pre-image.

 

The perimeter of the the pre-image is 20 (if you put the diagonals in the rhombus, you will form four right triangles and you can solve the one side of the rhombus by Pythagorean Theorem.)

 

Then 20*8 = 160 ft.

 

I think this is the simplest way to answer your question.

 

Joel L.

Answer 2

Dear Vivi,

    Question:  What is the perimeter of rhombus RSTU?

 

Note:  All sides of a Rhombus are equal.

          The diagonals are perpendicular bisectors of each other.

 

Therefore,  perimeter=4(S), where S=side of a rhombus

 

1.  Start by drawing two rhombi, a small one and a large one.  The diagonal of the smaller is 6 feet and 8 feet.

 

"Bisect" means to cut in half, so half the 6 feet diagonal is 3 feet, and half of the 8 feet one is 4 feet.  Inside the

 

rhombus, you have a right triangle that has a side of 4 feet, and another leg of 3 feet.  This means that the

 

hypotenuse is 5 feet. If you don't have this triplet memorized, then just use the Pythagorean Theorem.   The fact

 

that we are given a scale factor to multiply the small side to get the large side of the dilated rhombus, means that

 

both these objects are similar.  Now just multiply the side of 5 by 8 to get the large side on the dilated rhombus. 

 

     The large side is 40 feet long.  Now you need the perimeter of the large rhombus.  All sides of the rhombus will

 

be 40 feet.  Therefore, p=4*S.       p=_____________ I will let you complete this problem.

 

     If I have helped you, please give me a thumbs up.

                                                                     Susan C.