Question
Identify the whole-number measure of segment AD¯¯¯¯¯¯¯¯
that would create △ABD
and △ACD
as shown.
An illustration shows a rhombus where the vertices are labeled as follows: A on the top vertex, B on the left, C on the right, and D at the bottom. A dashed line is drawn from A to D. The sides are labeled as follows: A C is labeled as 5, A B as 4, B D as 8, and C D as 15.
(1 point)
Responses
5
5
9
9
11
11
12
12
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To create triangles ABD and ACD, we need to find the length of segment AD.
We can see from the given lengths that segment AD is the diagonal of the rhombus.
In a rhombus, the diagonals are perpendicular bisectors of each other. This means that they divide the rhombus into four congruent right triangles.
Since we are given the lengths of the other sides AC and BD, we can use the Pythagorean theorem to find the length of AD.
Using AC = 5 and BD = 8:
(AC)^2 + (BD)^2 = (AD)^2
5^2 + 8^2 = (AD)^2
25 + 64 = (AD)^2
89 = (AD)^2
Taking the square root of both sides, we find:
AD = √89
The whole-number measure of segment AD is not provided in the options.
pick 5 9 11 or 12 bruh
I apologize for the confusion. In this case, the closest whole-number measure of segment AD is 9.
The measure of two sides of a triangle are 7 and 11. Determine the range of values for the third side of the triangle.(1 point)
<n<
To determine the range of values for the third side of the triangle, we can use the triangle inequality theorem.
According to the theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the two given sides have lengths 7 and 11.
So we can set up the following inequality:
7 + 11 > x
Where x represents the length of the third side.
Simplifying the inequality, we get:
18 > x
Therefore, the range of values for the third side of the triangle is:
x < 18
The measures of two sides of a triangle are 5.2 and 8.1. Determine the range of values for the third side of the triangle.(1 point)
<n<
To determine the range of values for the third side of the triangle, we can use the triangle inequality theorem.
According to the theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the two given sides have lengths 5.2 and 8.1.
So we can set up the following inequality:
5.2 + 8.1 > x
Where x represents the length of the third side.
Simplifying the inequality, we get:
13.3 > x
Therefore, the range of values for the third side of the triangle is:
x < 13.3