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The diagonal of a rectangle is 25 cm and one of its sides is 15 cm. The area of the rectangle (in cm²) is:
300
375
250
400
300
Use the 3:4:5 Pythagorean triple scaled by 5 (15:20:25) to instantly find the other side as 20 cm without tedious calculation.
Diagonal of the rectangle d = 25 cm, and one side a = 15 cm
d=a2+b2,Area=a×b
Use the 3:4:5 Pythagorean triple scaled by 5 (15:20:25) to instantly find the other side as 20 cm without tedious calculation.
Students often add the squares of the diagonal and side instead of subtracting when finding the unknown side length.
Identify Given Values
Note down the diagonal and side length given in the problem statement.
d=25 cm,a=15 cm
Calculate the Second Side
Apply the Pythagorean theorem or recognize the scaled 3:4:5 ratio (3×5,4×5,5×5).
b=252−152=625−225=20 cm
Compute the Area
Multiply length and breadth to find the total area of the rectangle.
Area=15×20=300 cm2
A is correct because the calculated area of the rectangle is 300 cm².
Recognizing standard Pythagorean triples can speed up calculations in coordinate geometry and right-angled triangle problems.
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