Amanda is resizing a rectangular picture on her computer. The original picture has a length of 8 in and a width of 5 in. If she wants to keep it proportional, but have the new length be 4 in, what should be the new width?
A.
10.0 in
B.
2.0 in
C.
7.5 in
D.
2.5 in
B. 2.0 in
Since Amanda wants to keep the picture proportional, she can use the ratio of the original length to the new length to find the new width:
Original length / new length = Original width / new width
8 in / 4 in = 5 in / new width
2 = 5 / new width
new width = 5 / 2 = 2.5 in
Therefore, the new width should be 2.5 in to keep the picture proportional.
Which of the following is true about similar figures?
A.
Similar figures have congruent corresponding angles.
B.
Similar figures have the same size but different shapes.
C.
Similar figures have the same size and shape.
D.
The corresponding angles of similar figures are proportional; not congruent.
A. Similar figures have congruent corresponding angles.
Similar figures are figures that have the same shape but not necessarily the same size. The corresponding angles of similar figures are congruent, meaning they have the same measure. This is a key property of similar figures and is what distinguishes them from congruent figures.
In the figure above, triangle ABC is similar to triangle ADE. If side BC = 4 cm, side DE = 6 cm and side AE = 9 cm, then what is the measure of side AC?
A.
8 cm
B.
4.5 cm
C.
3 cm
D.
6 cm
Since the triangles ABC and ADE are similar, the corresponding sides are proportional.
BC/DE = AC/AE
Substitute the given values:
4 cm / 6 cm = AC / 9 cm
Solve for AC:
AC = (4 cm * 9 cm) / 6 cm
AC = 36 cm / 6 cm
AC = 6 cm
Therefore, the measure of side AC is 6 cm. Answer choice D.
In the diagram below, figure KLMN is similar to figure GHIJ.
Which of the following proportions can be used to find the value of n?
A. n/11 = 15/5
B. 15/n = 11/5
C. 11/n = 15/5
D. n/5 = 15/11
The correct proportion that can be used to find the value of n is:
B. 15/n = 11/5
This is because when dealing with similar figures, the corresponding sides are proportional. In this case, side KL corresponds to side GH, side LM corresponds to side HI, and side MN corresponds to side IJ.
For the proportion, we have:
KL (15) / GH (11) = LM (n) / HI (5)
15 / 11 = n / 5
Cross multiply:
15 * 5 = 11n
75 = 11n
n = 75 / 11
n = 6.82
Therefore, using the proportion 15/n = 11/5, we can find the value of n to be approximately 6.82.