9514 1404 393
Answer:
FH = 16
Explanation:
ΔGHE is a 5-12-13 triangle.
ΔEHF is a 3-4-5 triangle with a scale factor of 4, so side FH is 4·4 = 16 units.
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(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) are all commonly used Pythagorean triples. The first two on the list are used in these triangles.
If you like, you can work out the numbers using the Pythagorean theorem, which tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.
For ΔEHG, that is ...
GE² = EH² + HG²
13² = EH² + 5²
EH² = 13² -5² = 169 -25 = 144
And for ΔEHF, ...
FE² = EH² +HF²
20² = 144 + HF²
400 -144 = HF² = 256
HF = √256 = 16
The length of side FH is 16 units.