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Answer:
a = b = 28/√2
Step-by-step explanation:
The ratios of side lengths in an isosceles right triangle are ...
1 : 1 : √2 = a : b : 28
If we multiply the first ratio numbers by 28/√2, we get ...
1 : 1 : √2 = (28/√2) : (28/√2) : 28
That is, ...
a = b = 28/√2
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<em>Alternate solution</em>
Once you realize the triangle is isosceles, so that a=b, then you can use the Pythagorean theorem.
a^2 + a^2 = 28^2
2a^2 = 28^2 . . . . . . simplify
a√2 = 28 . . . . . take the positive square root
a = b = 28/√2