Option D: 64 is the length of x
Explanation:
The altitude of the triangle is 48
The two segments of the triangle are x and 36
From the figure, it is obvious that the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments.
Thus, by similar right triangles, we have,
[tex]\frac{36}{48} =\frac{48}{x}[/tex]
Multiplying both sides by x, we get,
[tex]\frac{36x}{48} =\frac{48x}{x}[/tex]
Simplifying, we have,
[tex]\frac{36x}{48} =48[/tex]
Multiplying both sides of the equation by 48, we get,
[tex]36x=1296[/tex]
Dividing both sides of the equation by 36, we have,
[tex]x=64[/tex]
Thus, the length of x is 64.
Therefore, the missing length is 64.
Hence, Option D is the correct answer.
