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
To create triangles ABD and ACD, we need to find the length of segment AD.
First, we know that triangle ABD is a right triangle because it is formed by the rhombus's diagonals. By using the Pythagorean theorem, we can find the length of AD.
We can calculate it as:
AD^2 = AB^2 + BD^2
AD^2 = 4^2 + 8^2
AD^2 = 16 + 64
AD^2 = 80
Taking the square root of both sides, we get:
AD = √80
Since the question asks for the whole-number measure of segment AD, we need to simplify √80.
√80 = √(16 * 5)
√80 = √16 * √5
√80 = 4 * √5
√80 = 4√5
Therefore, the whole-number measure of segment AD is 4√5.
simplify
To simplify 4√5, we can multiply the whole number (4) with the simplified radical (√5).
So, the simplified form of 4√5 is 4√5.