Which scale drawing is a dilation that increased the size of the original object it represents?
Figure 1: Chair
Figure 2: Tree
Figure 3: Nut (From a Nut Bolt)
Figure 4: House
Figure 4: House
What is the length of x in decimal form to the nearest hundredth?
____ Inches
I'm sorry, but without additional information or context, I cannot determine the length of x.
There's a small triangle with a length of 11.4 in. and the width of 18 in. And a bigger triangle with x length and the width of 23.4 in.
To find the length of x, we can use the concept of similar triangles and set up a proportion.
The ratio of the lengths of the corresponding sides of similar triangles is equal. In this case, we can set up the following proportion:
11.4 / 18 = x / 23.4
To solve for x, we can cross-multiply and divide:
(11.4 * 23.4) / 18 = x
263.16 / 18 = x
x ≈ 14.62
Therefore, the length of x, to the nearest hundredth, is approximately 14.62 inches.
What is the ratio of the area of the smaller triangle in relation to the area of the larger triangle?
There's a small triangle with the coordinates of (12, 6) (10, 2) (12, 2). And a bigger triangle with the coordinates of (5, 9) (2, 3) (5, 3).
To find the ratio of the areas, we need to calculate the area of both triangles. We can use the formula for finding the area of a triangle given its coordinates.
For the small triangle:
A = 0.5 * [(x1 * (y2 - y3)) + (x2 * (y3 - y1)) + (x3 * (y1 - y2))]
A = 0.5 * [(12 * (2 - 2)) + (10 * (2 - 6)) + (12 * (6 - 2))]
A = 0.5 * [(0) + (-20) + (24)]
A = 0.5 * (4) = 2 square units
For the larger triangle:
A = 0.5 * [(x1 * (y2 - y3)) + (x2 * (y3 - y1)) + (x3 * (y1 - y2))]
A = 0.5 * [(5 * (3 - 3)) + (2 * (3 - 9)) + (5 * (9 - 3))]
A = 0.5 * [(0) + (-12) + (30)]
A = 0.5 * (18) = 9 square units
The ratio of the area of the smaller triangle to the larger triangle is 2/9.