To find the scale factor, you can divide the side length of the larger square by the side length of the smaller square:
Scale factor = 20 units / 8 units = 2.5
Therefore, the scale factor you should use to dilate the square is 2.5.
Question
If you would like to dilate a square with a side length of 8 units to create a square with a side length of 20 units, what scale factor should you use? Write your answer in decimal form.(1 point)
11 answers
You use scale factor of 34 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle?(1 point)
inches
inches
To find the radius of the original circle, you can divide the radius of the dilated circle by the scale factor:
Original radius = 9 inches / 34 = 0.2647 inches
Therefore, the radius of the original circle was approximately 0.2647 inches.
Original radius = 9 inches / 34 = 0.2647 inches
Therefore, the radius of the original circle was approximately 0.2647 inches.
Use the image to answer the question.
An illustration shows two triangles, one big and one small. In the small triangle, one side measures 11.4 inches and another side measures 18 inches. In the big triangle, the side corresponding to 11.4 inches in the small triangle measures x and the side corresponding to 18 inches measures 23.4 inches.
What is the length of x in decimal form to the nearest hundredth?
(1 point)
inches
An illustration shows two triangles, one big and one small. In the small triangle, one side measures 11.4 inches and another side measures 18 inches. In the big triangle, the side corresponding to 11.4 inches in the small triangle measures x and the side corresponding to 18 inches measures 23.4 inches.
What is the length of x in decimal form to the nearest hundredth?
(1 point)
inches
To find the length of x in the big triangle, we can set up a proportion:
11.4 / 18 = x / 23.4
Cross multiplying:
11.4 * 23.4 = 18x
266.76 = 18x
x = 14.82 inches
Therefore, the length of x in the big triangle to the nearest hundredth is 14.82 inches.
11.4 / 18 = x / 23.4
Cross multiplying:
11.4 * 23.4 = 18x
266.76 = 18x
x = 14.82 inches
Therefore, the length of x in the big triangle to the nearest hundredth is 14.82 inches.
△CDE∼△PQR . m∠C=13° , m∠D=65° . What are the measures of angles P , Q , and R ?(2 points)
m∠P =
°, m∠Q =
° and m∠R=
°
m∠P =
°, m∠Q =
° and m∠R=
°
Since triangles CDE and PQR are similar, the corresponding angles are equal.
m∠C = m∠P = 13°
m∠D = m∠Q = 65°
To find m∠R, we can use the property that the sum of the angles in a triangle is 180°:
m∠R = 180° - m∠P - m∠Q
m∠R = 180° - 13° - 65°
m∠R = 102°
Therefore, the measures of angles in triangle PQR are:
m∠P = 13°
m∠Q = 65°
m∠R = 102°
m∠C = m∠P = 13°
m∠D = m∠Q = 65°
To find m∠R, we can use the property that the sum of the angles in a triangle is 180°:
m∠R = 180° - m∠P - m∠Q
m∠R = 180° - 13° - 65°
m∠R = 102°
Therefore, the measures of angles in triangle PQR are:
m∠P = 13°
m∠Q = 65°
m∠R = 102°
△XYZ∼△RST. m∠X=50°, m∠S=79°. What is the measure of angle T?(1 point)
m∠T =
°
m∠T =
°
Since triangles XYZ and RST are similar, the corresponding angles are equal.
m∠X = m∠R
50° = m∠R
To find m∠T, we can use the fact that the sum of the angles in a triangle is 180°:
m∠T = 180° - m∠R - m∠S
m∠T = 180° - 50° - 79°
m∠T = 51°
Therefore, the measure of angle T is:
m∠T = 51°
m∠X = m∠R
50° = m∠R
To find m∠T, we can use the fact that the sum of the angles in a triangle is 180°:
m∠T = 180° - m∠R - m∠S
m∠T = 180° - 50° - 79°
m∠T = 51°
Therefore, the measure of angle T is:
m∠T = 51°
Given △ABC∼△DEF , m∠A=52° , and m∠E=11° , what is the measure of angle C ?(1 point)
m∠C =
°
m∠C =
°
Since triangles ABC and DEF are similar, the corresponding angles are equal.
m∠A = m∠D = 52°
To find m∠C, we can use the fact that the sum of the angles in a triangle is 180°:
m∠C = 180° - m∠A - m∠B
m∠C = 180° - 52° - 90°
m∠C = 38°
Therefore, the measure of angle C is:
m∠C = 38°.
m∠A = m∠D = 52°
To find m∠C, we can use the fact that the sum of the angles in a triangle is 180°:
m∠C = 180° - m∠A - m∠B
m∠C = 180° - 52° - 90°
m∠C = 38°
Therefore, the measure of angle C is:
m∠C = 38°.