How to find if rectangles are similar - ACT Math
Card 0 of 3
The width of a rectangle is 5 times the length of the rectangle. The width of the rectangle is 30. What is the perimeter of the rectangle?
The width of a rectangle is 5 times the length of the rectangle. The width of the rectangle is 30. What is the perimeter of the rectangle?
If the width is 5 times the length, and the width is 30, then the length is 6. The perimeter of a rectangle is 2 x width + 2 x length. 2 x 30 + 2 x 6 = 72.
If the width is 5 times the length, and the width is 30, then the length is 6. The perimeter of a rectangle is 2 x width + 2 x length. 2 x 30 + 2 x 6 = 72.
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Two rectangles are similar. The perimeter of the first rectangle is 36. The perimeter of the second is 12. If the base length of the second rectangle is 4, what is the height of the first rectangle?
Two rectangles are similar. The perimeter of the first rectangle is 36. The perimeter of the second is 12. If the base length of the second rectangle is 4, what is the height of the first rectangle?
Solve for the height of the second rectangle.
Perimeter = 2B + 2H
12 = 2(4) + 2H
12 = 8 + 2H
4 = 2H
H = 2
If they are similar, then the base and height are proportionally equal.
B1/H1 = B2/H2
4/2 = B2/H2
2 = B2/H2
B2 = 2H2
Use perimeter equation then solve for H:
Perimeter = 2B + 2H
36 = 2 B2 + 2 H2
36 = 2 (2H2) + 2 H2
36 = 4H2 + 2 H2
36 = 6H2
H2 = 6
Solve for the height of the second rectangle.
Perimeter = 2B + 2H
12 = 2(4) + 2H
12 = 8 + 2H
4 = 2H
H = 2
If they are similar, then the base and height are proportionally equal.
B1/H1 = B2/H2
4/2 = B2/H2
2 = B2/H2
B2 = 2H2
Use perimeter equation then solve for H:
Perimeter = 2B + 2H
36 = 2 B2 + 2 H2
36 = 2 (2H2) + 2 H2
36 = 4H2 + 2 H2
36 = 6H2
H2 = 6
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Two rectangles are similar. The first rectangle has a perimeter of 
and the second has a perimeter of 
. If the first rectangle has a length of 
, what the length of the second rectangle?
Two rectangles are similar. The first rectangle has a perimeter of
1. Create a proportion comparing the two given rectangles:
2. Solve for the length of the second rectangle by cross-multiplying:
1. Create a proportion comparing the two given rectangles:
2. Solve for the length of the second rectangle by cross-multiplying:
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