Pythagoras Theorem — Maharashtra (SSC) Class 10 Mathematics Solutions (Free)
Free step-by-step Maharashtra (SSC) Class 10 Mathematics solutions for "Pythagoras Theorem" — important questions with detailed answers, download PDF for board exam preparation.
TL;DR: Free step-by-step Maharashtra (SSC) Class 10 Mathematics solutions for "Pythagoras Theorem" — important questions with detailed answers, download PDF…
By Syllab.in · Updated
Q1: In right triangle ABC with right angle at B, AB = 3 cm and BC = 4 cm. Find AC.
Step 1: Apply Pythagoras theorem. In right triangle, (Hypotenuse)^2 = (Base)^2 + (Height)^2.
Step 2: AC is the hypotenuse (opposite to right angle). AC^2 = AB^2 + BC^2.
Step 3: Substitute values. AC^2 = 3^2 + 4^2 = 9 + 16 = 25.
Step 4: Take square root. AC = sqrt(25) = 5 cm.
Step 5: Verify using Pythagorean triplet. (3, 4, 5) is a well-known Pythagorean triplet.
Answer: AC = 5 cm.
Q2: A ladder of length 13 m leans against a wall. The base of the ladder is 5 m from the wall. How high does the ladder reach on the wall?
Step 1: Set up the problem as a right triangle. Ladder (hypotenuse) = 13 m, distance from wall (base) = 5 m, height on wall = h.
Step 2: Apply Pythagoras theorem. (Hypotenuse)^2 = (Base)^2 + (Height)^2.
Step 3: 13^2 = 5^2 + h^2.
Step 4: 169 = 25 + h^2.
Step 5: Solve for h^2. h^2 = 169 - 25 = 144.
Step 6: Take square root. h = sqrt(144) = 12 m.
Step 7: Verify. 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Correct.
Answer: The ladder reaches 12 m high on the wall.
Q3: Check if a triangle with sides 6 cm, 8 cm, and 10 cm is a right triangle.
Step 1: Identify the longest side (potential hypotenuse). Longest side = 10 cm.
Step 2: Apply Pythagoras theorem check. If 6^2 + 8^2 = 10^2, then it's a right triangle.
Step 3: Calculate. 6^2 + 8^2 = 36 + 64 = 100.
Step 4: Calculate hypotenuse squared. 10^2 = 100.
Step 5: Compare. 100 = 100, so the equation is satisfied.
Step 6: Conclusion. Since the sum of squares of two sides equals the square of the third side, it is a right triangle.
Answer: Yes, it is a right triangle. The right angle is op…
Q4: In right triangle PQR with right angle at Q, PQ = 7 cm and QR = 24 cm. Find PR and verify.
Step 1: Identify the hypotenuse. PR is opposite the right angle at Q, so PR is the hypotenuse.
Step 2: Apply Pythagoras theorem. PR^2 = PQ^2 + QR^2.
Step 3: Substitute. PR^2 = 7^2 + 24^2 = 49 + 576 = 625.
Step 4: Take square root. PR = sqrt(625) = 25 cm.
Step 5: Verify the calculation. 7^2 + 24^2 = 49 + 576 = 625. sqrt(625) = 25. Correct.
Step 6: Check if it's a Pythagorean triplet. (7, 24, 25) is a Pythagorean triplet.
Answer: PR = 25 cm.
Q5: Two vertical poles of heights 4 m and 9 m stand on a level ground 12 m apart. Find the distance between their tops.
Step 1: Set up coordinate system. Place base of first pole at origin (0, 0) and base of second at (12, 0).
Step 2: Position of top of first pole: (0, 4). Position of top of second pole: (12, 9).
Step 3: Find distance using distance formula or by creating a right triangle.
Step 4: Horizontal distance = 12 m. Vertical distance = 9 - 4 = 5 m.
Step 5: Apply Pythagoras theorem. Distance^2 = 12^2 + 5^2 = 144 + 25 = 169.
Step 6: Distance = sqrt(169) = 13 m.
Answer: The distance between the tops is 13 m…
Showing 5 of 8 questions — full solutions on the page.