A rectangle has a length of 25 cm and a width of 12.25 cm. A larger, similar rectangle has width 49 cm. What is the length of the larger rectangle?(1 point)
Responses
98 cm
98 cm
100 cm
100 cm
24.01 cm
24.01 cm
4 cm
To find the length of the larger rectangle, we can use the concept of similarity. Similar shapes have proportional sides.
If the original rectangle has a length of 25 cm and a width of 12.25 cm, we can find the ratio of the length to the width. The ratio is:
Length/Width = 25/12.25
Now, we can use this ratio to find the length of the larger rectangle. We know that the width of the larger rectangle is 49 cm. Setting up a proportion, we have:
25/12.25 = x/49
Cross-multiplying, we get:
12.25x = 25 * 49
Simplifying, we have:
12.25x = 1225
Dividing both sides by 12.25, we get:
x = 100
Therefore, the length of the larger rectangle is 100 cm.
△CDE∼△PQR . CD=9 m , EC=15 m , PQ=15 m . What is the length of RP¯¯¯¯¯¯¯¯ ?(1 point)
Responses
9 m
9 m
25 m
25 m
30 m
30 m
0.6 m
To find the length of RP¯¯¯¯¯¯¯¯, we can use the concept of similarity. Similar triangles have proportional sides.
Since △CDE∼△PQR, we can set up a proportion using corresponding sides. The corresponding sides are CD and PQ.
CD/PQ = DE/RP
We can substitute the given values into the proportion:
9/15 = 15/RP
Cross-multiplying, we get:
9 * RP = 15 * 15
Simplifying, we have:
9 * RP = 225
Dividing both sides by 9, we get:
RP = 25
Therefore, the length of RP¯¯¯¯¯¯¯¯ is 25 m.
Use the image to answer the question.
An illustration shows two quadrilaterals, one big and one small. The smaller quadrilateral is A B C D and the bigger one is H G F E.
Which statement represents the similarity between the two figures?
(1 point)
Responses
quadrilateral DCBA ∼ quadrilateral GEFH
quadrilateral upper D upper C upper B upper A tilde quadrilateral upper G upper E upper F upper H
quadrilateral ABCD ∼ quadrilateral HGFE
quadrilateral upper A upper B upper C upper D tilde quadrilateral upper H upper G upper F upper E
quadrilateral ABCD ∼ quadrilateral EFGH
quadrilateral upper A upper B upper C upper D tilde quadrilateral upper E upper F upper G upper H
quadrilateral DCBA ∼ quadrilateral HGFE
The correct statement that represents the similarity between the two figures is:
quadrilateral ABCD ∼ quadrilateral EFGH
quadrilateral upper A upper B upper C upper D tilde quadrilateral upper E upper F upper G upper H