- A225 cm
- B15 cm
- C21 cm
- D25 cm
Step-by-Step Solution
The square on the longest side has area , so the side is cm. The sides 9, 12, 15 form a Pythagorean triplet.
Answer: B) 15 cm
Squares are drawn on the three sides of a right triangle. The areas of the two smaller squares are shown. How long is the longest side of the triangle?
Class 8Squares and Square RootsSquares and Roots
Key idea: Properties of perfect squares
Useful patterns to spot a perfect square (and reject non-squares):
- **Last digit**: a perfect square ends in 0, 1, 4, 5, 6, or 9 — NEVER in 2, 3, 7, or 8. So 142 cannot be a perfect square (ends in 2).
- **Number of zeros at the end**: must be even. 100 is a perfect square ; 1000 is not.
- **Squares of even numbers are even; squares of odd numbers are odd.**
- **Sum of consecutive odd numbers**: 1 + 3 + 5 + … + . Try it: .
These let you reject many candidates without doing any heavy work.
- **Last digit**: a perfect square ends in 0, 1, 4, 5, 6, or 9 — NEVER in 2, 3, 7, or 8. So 142 cannot be a perfect square (ends in 2).
- **Number of zeros at the end**: must be even. 100 is a perfect square ; 1000 is not.
- **Squares of even numbers are even; squares of odd numbers are odd.**
- **Sum of consecutive odd numbers**: 1 + 3 + 5 + … + . Try it: .
These let you reject many candidates without doing any heavy work.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Squares and Square Roots practice questions
More Class 8 Squares and Square Roots practice
This long division finds √5476. The same digit goes in both orange boxes. What is √5476?On the number line, 250 lies between two perfect squares. What is √250, correct to the…A square hall floor is covered with 2025 identical square tiles. The tiles along the…The number line shows 1,300 and the two perfect squares closest to it. What is the least…Which pairing of number and its square root is INCORRECT?