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Ada is <u>incorrect</u>, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.
For Rectangle PQRS:-
By Pythagoras Theorem, in right triangle PQS,
SQ² = PQ² + PS²,
or, SQ² = 8² + 16² sq. inches,
or, SQ² = 64 + 256 sq. inches,
or, SQ = √320 sq. inches,
or, SQ = 8√5 inches.
Thus, the length of diagonal SQ, of rectangle PQRS is 8√5 inches.
For Square LMNO:-
By Pythagoras Theorem, in right triangle LMO,
OM² = LM² + LO²,
or, OM² = 8² + 8² sq. inches,
or, OM² = 64 + 64 sq. inches,
or, OM = √128 sq. inches,
or, OM = 8√2 inches.
Thus, the length of diagonal OM, of square LMNO is 8√2 inches.
We know that 2*OM ≠ SQ, as 2*8√2 ≈ 8√5.
Thus, Ada is <u>incorrect</u>, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.
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