Pythagoras theorem and its converse MCQs

Q1. A rectangular field is 8 m by 15 m. Find (perimeter + a diagonal):

• A.120
• B.40
• C.46
• D.63

Answer: D. 63

Data from the problem: 8 m; 15 m. We need: Find (perimeter + a diagonal). Governing law - Diagonal = sqrt(8^2+15^2). This is the equation that links the given quantities to the unknown (math, chapter 'Triangles'). Substituting: Diagonal = sqrt(8^2+15^2) → perimeter = 2(8+15) → sum = 63 m. Therefore the answer is D) 63. Where the distractors go off: option A) '120' doesn't hold - Wrong: a common multi-step slip gives this; option B) '40' doesn't hold - Wrong: uses an incorrect intermediate value; option C) '46' is wrong because Wrong: a step was skipped or HCF/LCM swapped.

Q2. A rectangular field is 12 m by 16 m. Find (perimeter + a diagonal):

• A.76
• B.192
• C.48
• D.56

Answer: A. 76

We are told: 12 m; 16 m. Target quantity: Find (perimeter + a diagonal). Formula - Diagonal = sqrt(12^2+16^2). This is the equation that links the given quantities to the unknown (math, chapter 'Triangles'). Plugging the values in: Diagonal = sqrt(12^2+16^2) → perimeter = 2(12+16) → sum = 76 m. Thus the answer is A) 76. Wrong options at a glance: option B) '192' fails since Wrong: a common multi-step slip gives this; option C) '48' misses the point - Wrong: uses an incorrect intermediate value; option D) '56' doesn't hold - Wrong: a step was skipped or HCF/LCM swapped.

Q3. A rectangular field is 20 m by 21 m. Find (perimeter + a diagonal):

• A.82
• B.111
• C.420
• D.70

Answer: B. 111

Reading the problem, 20 m, 21 m (math, chapter 'Triangles'). The unknown we need is Find (perimeter + a diagonal). This is a classic application of Diagonal = sqrt(20^2+21^2). Putting the numbers in: Diagonal = sqrt(20^2+21^2) → perimeter = 2(20+21) → sum = 111 m. Matching this against the options, B) 111 is the answer. As for the others, option A) '82' is wrong because Wrong: a step was skipped or HCF/LCM swapped; option C) '420' doesn't hold - Wrong: a common multi-step slip gives this.