Use the image to answer the question.
An illustration shows two triangles, one big and one small. In the big triangle, one side measures 13 yards and another side measures x. In the small triangle, the side corresponding to 13 yards in the big triangle measures 3.25 yards and the side corresponding to x measures 4.23 yards.
Use proportions to find the missing side length ( x ) in the two similar figures.
(1 point)
Responses
4 yards
4 yards
9.99 yards
9.99 yards
16.92 yards
16.92 yards
1.05 yards
The missing side length x can be found by setting up a proportion:
x / 13 = 4.23 / 3.25
Cross multiplying, we get:
3.25x = 13 * 4.23
3.25x = 55.19
x = 55.19 / 3.25
x ≈ 16.92
Therefore, the missing side length x is approximately 16.92 yards.
The correct answer is: 16.92 yards
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
24.01 cm
24.01 cm
4 cm
4 cm
98 cm
To find the length of the larger rectangle, we can set up a proportion based on the ratio of corresponding sides in similar figures:
25 / 12.25 = x / 49
Cross multiply:
25 * 49 = 12.25x
1225 = 12.25x
Divide both sides by 12.25:
x ≈ 100
Therefore, the length of the larger rectangle is approximately 100 cm.
The correct answer is: 100 cm
Question
△CDE∼△PQR. CD=9 m, EC=15 m, PQ=15 m. What is the length of RP¯¯¯¯¯¯¯¯?(1 point)
Responses
30 m
30 m
25 m
25 m
0.6 m
0.6 m
9 m
To find the length of RP in triangle PQR, we can set up a proportion based on the corresponding sides in similar triangles:
RP / CD = PQ / EC
Substitute the given values:
RP / 9 = 15 / 15
Solve for RP:
RP = 9
Therefore, the length of RP is 9 meters.
The correct answer is: 9 meters
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 ABCD ∼ quadrilateral HGFE
quadrilateral upper A upper B upper C upper D tilde quadrilateral upper H upper G upper F upper E
quadrilateral DCBA ∼ quadrilateral HGFE
quadrilateral upper D upper C upper B upper A tilde quadrilateral upper H upper G upper F upper E
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 EFGH
The correct statement that represents the similarity between the two figures is:
quadrilateral ABCD ∼ quadrilateral HGFE
This indicates that quadrilateral ABCD is similar to quadrilateral HGFE.
If △PQR∼△JKL, which statements are correct?(1 point)
Responses
∠Q≅∠K and PR¯¯¯¯¯¯¯¯ corresponds to JL¯¯¯¯¯¯¯.
angle upper Q congruent to angle upper K and Modifying above upper P upper R with bar corresponds to Modifying above upper J upper L with bar .
∠P≅∠J and QR¯¯¯¯¯¯¯¯ corresponds to JK¯¯¯¯¯¯¯¯.
angle upper P congruent to angle upper J and Modifying above upper Q upper R with bar corresponds to Modifying above upper J upper K with bar .
∠P≅∠J and PQ¯¯¯¯¯¯¯¯ corresponds to JL¯¯¯¯¯¯¯.
angle upper P congruent to angle upper J and Modifying above upper P upper Q with bar corresponds to Modifying above upper J upper L with bar .
∠Q≅∠L and PQ¯¯¯¯¯¯¯¯ corresponds to JK¯¯¯¯¯¯¯¯.
The correct statement is:
∠Q ≅ ∠K and PR corresponds to JL.
This statement correctly indicates the angle congruence and the corresponding sides between the similar triangles △PQR and △JKL.