40.6k views
0 votes
Ezekiel decomposed the rectangle shown into three smaller rectangles. Then he demonstrated the Distributive Property by modeling the area of the entire rectangle in terms of the three smaller rectangles. Which equation could Ezekiel have used?

answer choices:
1. 21(3 + 3) = 21(3) + 21(3)
2. 6(6 + 12 + 3) = 6(6) + 6(12) + 6(3)
3. 21(3 + 2 + 3) = 21(3) + 21(2) + 21(3)
4. 6(10 + 10 + 11) = 6(10) + 6(10) + 6(11)

Ezekiel decomposed the rectangle shown into three smaller rectangles. Then he demonstrated-example-1
User Kateria
by
4.3k points

1 Answer

1 vote

Answer:

2. 6(6+12+3) = 6(6)+6(12) + 6(3) = 36+72 + 18 = 126 unit square

Area = 126 unit square.

and satisfies the 3 rectangle area. However can such amounts fit inside the rectangle as distributable?

We prove length of 21 units =

21-6 = 15 Units length and 15 - 12 = 3. Proves all 3 measures of length does fit within the length of 21 units length

Conclusion Does satisfy as three length measures within one larger measure given for the large rectangle fit exact, to find area identical in totals.

Explanation:

Proof area of 21 x 6 area rectangle = 126unit square

3 smaller rectangles made from same larger rectangle must = 126 unit square when all 3 smaller area are added together.

answer choices

1. 21(3+3) = 2(3)+21(3) only shows 2 rectangles area = 2 rectangles angle

Does not satisfy

2. 6(6+12+3) = 6(6)+6(12) + 6(3) = 36+72 + 18 = 126 unit square and satisfies the 3 rectangle area. However can such amounts fit inside the rectangle as distributable?

We prove length of 21 units =

21-6 = 15 Units length and 15 - 12 = 3. Proves it does fit within the width of 21 units length

Conclusion Does satisfy as three length measures within one larger measure given for the large rectangle fit exact, to find area identical in totals.

3. 21 (3+2+3) = 21 (3) +21 (2)+21 (3) does not satisfy 6 units width as 3+2+3 = 8 and is too high a number. Does not satisfy.

4.6(10+10+11) = 6(10) + 6(10) + 6(11) does not satisfy

The lengths of the three rectangles adds to 31 length as 10+10+11 = 31 instead of 21. Does not satisfy.

User Ked
by
4.0k points