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Answer:
C) a = 3√10; b = 3√5
Step-by-step explanation:
The side ratios in an isosceles right triangle are 1 : 1 : √2. This is a fact worth remembering. You know the triangle is isosceles because both acute angles are 45°, which means both legs are the same length.
If the leg lengths are 1, the Pythagorean theorem tells you the hypotenuse is ...
c^2 = a^2 + b^2 . . . . . . for legs a, b, and hypotenuse c
c^2 = 1^2 + 1^2 = 2
c = √2
This tells you the <em>leg : leg : hypotenuse</em> ratios are as shown above.
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What that means here is that b = 3√5, the same length as the one shown. It also means that ,,,
a = (3√5)(√2) = 3√(5·2)
a = 3√10
The only answer choice with the correct value of 'a' is (C).
a = 3√10, b = 3√5
