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
100 cm
100 cm
98 cm
98 cm
4 cm
4 cm
24.01 cm??
To find the length of the larger rectangle, we can use the concept of similarity between similar shapes.
Similar shapes have proportional sides.
In this case, the width of the larger rectangle is 49 cm, while the width of the smaller rectangle is 12.25 cm.
Since the sides are proportional, we can set up a proportion:
Length of larger rectangle / Width of larger rectangle = Length of smaller rectangle / Width of smaller rectangle
Let's substitute the given values into the proportion:
Length of larger rectangle / 49 cm = 25 cm / 12.25 cm
Next, cross multiply to solve for the length of the larger rectangle:
Length of larger rectangle = (25 cm / 12.25 cm) * 49 cm
Simplifying the expression, we get:
Length of larger rectangle = 100 cm (rounded to the nearest whole number)
Therefore, the length of the larger rectangle is 100 cm.
Sides of Similar Figures Quick Check
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Question
△CDE∼△PQR. CD=9 m, EC=15 m, PQ=15 m. What is the length of RP¯¯¯¯¯¯¯¯?(1 point)
Responses
25 m
25 m
9 m
9 m
30 m
30 m
0.6 m
Since △CDE∼△PQR, we know that the corresponding sides of the triangles are proportional.
In this case, CD corresponds to PQ. EC corresponds to QR.
We are given that CD = 9 m and PQ = 15 m.
To find the length of RP¯¯¯¯¯¯¯¯, we can set up a proportion using the corresponding sides:
RP / CD = QR / PQ
Substituting the given values into the proportion:
RP / 9 m = QR / 15 m
Next, cross multiply to solve for RP:
RP = (QR / 15 m) * 9 m
Since EC corresponds to QR, we are given that EC = 15 m. So, QR = 15 m.
Now, substituting QR = 15 m into the equation:
RP = (15 m / 15 m) * 9 m
Simplifying the expression, we get:
RP = 9 m
Therefore, the length of RP¯¯¯¯¯¯¯¯ is 9 m.
Which statement represents the similarity between the two figures?
(1 point)
Responses
quadrilateral DCBA ∼ quadrilateral HGFE
quadrilateral upper D upper C upper B upper A tilde quadrilateral upper H upper G upper F upper E
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 GEFH
The correct statement that represents the similarity between the two figures is:
quadrilateral ABCD ∼ quadrilateral HGFE
quadrilateral upper A upper B upper C upper D tilde quadrilateral upper H upper G upper F upper E