Answer:
a = 4.5 , b = 7.5
Explanation:
using Pythagoras' identity in the two right triangle
outer right triangle
b² + 10² = (8 + a)² = 64 + 16a + a² → (1)
inner right triangle
a² + 6² = b² → (2)
substitute b² = a² + 6² = a² + 36 into (1)
a² + 36 + 100 = 64 + 16a + a² ( subtract a² from both sides )
136 = 64 + 16a ( subtract 64 from both sides )
72 = 16a ( divide both sides by 16 )
4.5 = a
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substitute a = 4.5 into (2)
4.5² + 6² = b² , that is
20.25 + 36 = b²
56.25 = b² ( take square root of both sides )
= b , then
b = 7.5