Answer:
d. 9.4 feet
Explanation:
You want the measure of long side XY of the right triangle that has its altitude dividing the hypotenuse into segments 3 and 8 feet in length.
Similarity
In this geometry, all of the right triangles are similar. That means the ratio of long side to hypotenuse is the same for all of the triangles:
XY/(3+8) = 8/XY
XY² = (3+8)(8)
XY = √88 ≈ 9.4
The length of segment XY is about 9.4 feet.
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Additional comment
As we see here, the long side of the large triangle is the root of the product of the long segment of the hypotenuse with the whole hypotenuse:
XY=√(8(8+3)) = √88
The same relation works on the other side of the triangle. The short side of the large triangle is the root of the product of the short segment of the hypotenuse and the whole:
short side = √(3(11)) = √33
The relation for the altitude of the triangle is that it is the root of the product of the two hypotenuse segments:
altitude = √(3·8) = √24