Area and Similarity: Practice Level 3 | Geometry

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

Two similar polygons have perimeter ratio $\sqrt7:3$ , in that order. What is their area ratio in the same order?

Answer choices for question 1 A $\sqrt7:3$ B $49:9$ C $9:7$ D $7:9$
2

Two similar images of one original polygon use length factors $2/3$ and $5/6$ . What is the first-image to second-image area ratio?

Answer choices for question 2 A $4:5$ B $16:25$ C $25:16$ D $2:5$
3

Similar polygons have original area $49\text{ cm}^2$ and image area $196\text{ cm}^2$ . An original side is $x$ cm and its corresponding image side is $(x+4)$ cm. What is the positive value of $x$ ?

Answer choices for question 3 A $8$ B $12$ C $4$ D $2$
4

A similar image has length factor $5/3$ and area $128\text{ cm}^2$ greater than the original. What is the image area?

Answer choices for question 4 A $200\text{ cm}^2$ B $72\text{ cm}^2$ C $320\text{ cm}^2$ D $512/3\text{ cm}^2$
5

A simple polygon is resized by length factor $3/5$ , then its image is resized by length factor $5/4$ . What is the final-to-original area factor?

Answer choices for question 5 A $3/4$ B $16/9$ C $9/16$ D $15/16$
6

A similar image has $125\%$ more area than the original. What number multiplies an original length to give its corresponding image length?

Answer choices for question 6 A $5/4$ B $3/2$ C $9/4$ D $\sqrt5/2$
7

Similar polygons have original area $52\text{ cm}^2$ , image area $117\text{ cm}^2$ , and image perimeter $69$ cm. What is the original perimeter?

Answer choices for question 7 A $103.5$ cm B $92/3$ cm C $23$ cm D $46$ cm
8

A nonoverlapping triangle partition is carried through a similarity of positive length factor k. Which expression gives the image area if the original triangle areas are a, b, and c?

Answer choices for question 8 A $k^2(a+b+c)$ B $k(a+b+c)$ C $k^2a+b+c$ D $(ka+kb+kc)^2$
9

For similar polygons, the image perimeter is $1.1$ times the original. Which image-area statement follows?

Answer choices for question 9 A The image has $10\%$ more area B The image has $21\%$ more area C The image has $11\%$ more area D The image has $110\%$ more area
10

A polygonal frame consists of an outer region of area $80\text{ cm}^2$ with a polygonal hole of area $12\text{ cm}^2$ . The whole frame is resized by length factor $1/2$ . What is the area of the material in the image?

Answer choices for question 10 A $34\text{ cm}^2$ B $20\text{ cm}^2$ C $17\text{ cm}^2$ D $8\text{ cm}^2$
11

Two nondegenerate triangles are known to be similar. Their corresponding altitudes have equal positive lengths. Which conclusion must hold?

Answer choices for question 11 A They are congruent and have equal areas B They have equal areas but cannot be congruent C Their area ratio is 2:1 D Only their perimeters, not their areas, are equal
12

Similar polygons have original area $48\text{ cm}^2$ and image area $147\text{ cm}^2$ . An image side is $35$ cm. What is the corresponding original side?

Answer choices for question 12 A $61.25$ cm B $80/7$ cm C $49$ cm D $20$ cm