The rectangle below is dilated by a scale factor of 2. Find the perimeter and area of the rectangle below, as well as the perimeter and area of the dilated rectangle. Express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). Figures are not necessarily drawn to scale.
The height of the small rectangle is 3 and the length of it is 2
Perimeter of given rectangle ? units
Perimeters dilated rectangle ? units
Area of given rectangle ? units^2
Area of dilated rectangle ? units^2
Given rectangle:
Height = 3 units
Length = 2 units
Perimeter of given rectangle = 2(3) + 2(2) = 6 + 4 = 10 units
Area of given rectangle = 3 * 2 = 6 units^2
Dilated rectangle:
Height = 3 * 2 = 6 units
Length = 2 * 2 = 4 units
Perimeter of dilated rectangle = 2(6) + 2(4) = 12 + 8 = 20 units
Area of dilated rectangle = 6 * 4 = 24 units^2
Triangle DEF is similar to triangle GHI. Find the measure of side IG. Round your answer to the nearest tenth if necessary.
The slanted side of the bigger triangle is 13, and the length of the higher triangle is 18. The length of the smaller triangle is 5
For similar triangles, the ratio of corresponding sides is equal.
Given:
DE (smaller triangle) = 5
EF (smaller triangle) = 18
GH (larger triangle) = 13
Let x be the measure of side IG.
Using the ratio of corresponding sides:
DE/GH = EF/IG
5/13 = 18/x
Cross multiply:
5x = 13 * 18
5x = 234
x = 234/5
x = 46.8
Therefore, the measure of side IG is approximately 46.8 units.
This is wrong
Let's correct the calculation:
Given: DE = 5, GH = 13, EF = 18
We are solving for IG.
By the property of similar triangles:
DE/GH = EF/IG
Substitute the values:
5/13 = 18/IG
Cross multiply:
5 * IG = 13 * 18
5IG = 234
IG = 234 / 5
IG = 46.8
Therefore, the measure of side IG is exactly 46.8 units. Thank you for your patience.