13yd,x
3.25yd,4.23yd
Use proportions to find the missing side length ( x ) in the two similar figures.
4 yards
16.92 yards
1.05 yards
9.99 yards
To find the missing side length in the two similar figures using proportions, we can set up the following proportion:
$\frac{13}{3.25} = \frac{x}{4.23}$
To solve for x, we can cross multiply:
$13 \cdot 4.23 = 3.25 \cdot x$
$54.99 = 3.25 \cdot x$
Dividing both sides by 3.25:
$x = 16.92$ yards
Therefore, the missing side length x is 16.92 yards in the given figures.
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
24.01 cm
24.01 cm
4 cm
To find the length of the larger rectangle, we can set up the following proportion:
$\frac{25}{12.25} = \frac{x}{49}$
To solve for x, we can cross multiply:
$25 \cdot 49 = 12.25 \cdot x$
$1225 = 12.25 \cdot x$
Dividing both sides by 12.25:
$x = 100$ cm
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
0.6 m
0.6 m
25 m
25 m
30 m
30 m
9 m
To find the length of RP¯¯¯¯¯¯¯¯, we can set up the following proportion:
$\frac{CD}{EC} = \frac{PQ}{RP}$
Substituting the given values:
$\frac{9}{15} = \frac{15}{RP}$
Cross multiplying:
$9 \cdot RP = 15 \cdot 15$
$9 \cdot RP = 225$
Dividing both sides by 9:
$RP = 25$ m
Therefore, the length of RP¯¯¯¯¯¯¯¯ is 25 m in the given similar triangles.
If △PQR∼△JKL, which statements are correct?(1 point)
Responses
∠Q≅∠L and PQ¯¯¯¯¯¯¯¯ corresponds to JK¯¯¯¯¯¯¯¯.
angle upper Q congruent to angle upper L and Modifying above upper P upper Q with bar corresponds to Modifying above upper J upper K with bar .
∠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 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 .
∠P≅∠J and QR¯¯¯¯¯¯¯¯ corresponds to JK¯¯¯¯¯¯¯¯.
The correct statement is:
∠P≅∠J and PQ¯¯¯¯¯¯¯¯ corresponds to JL¯¯¯¯¯¯¯.
This means that angle P is congruent to angle J in the similar triangles, and the corresponding sides PQ¯¯¯¯¯¯¯¯ and JL¯¯¯¯¯¯¯ have the same ratio.