Pythagoras theorem
- Seg AM is a median of ∆ABC. If AB = 22, AC = 34, BC = 24, find AM. ∴ AM = 26 units 1
- Find the length of a diagonal of a rectangle having sides 11 cm and 60 cm. Answer: 61 cm A diagonal divides the rectangle into two right-angled triangles, with the sides of the rectangle as the legs and the diagonal... 1
- Do sides 7 cm, 24 cm, 25 cm form a right angled triangle? Give reason. The sides of the triangle are 7 cm, 24 cm and 25 cm. The longest side of the triangle is 25 cm. ∴ (25)² = 625 Now, sum of the squares of the... 1
- Find the height of an equilateral triangle having side 2a. Let ∆ABC be the given equilateral triangle. ∴ ∠B = 60° [Angle of an equilateral triangle] Let AD ⊥BC, B – D – C. In ∆ABD, ∠B = 60°, ∠ADB = 9... 1
- In the adjoining figure, ∠QPR = 90°, seg PM ⊥ seg QR and Q – M – R, PM = 10, QM = 8, find QR. In ∆PQR, ∠QPR = 90° and [Given] seg PM ⊥ seg QR ∴ PM² = OM × MR [by Theorem of geometric mean] ∴ 10² = 8 × MR ∴ MR = 100over8 = 12.5 Now, QR... 1
- In ∆PQR, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR. In ∆PQR, point S is the midpoint of side QR. [Given] ∴ seg PS is the median. ∴ PQ² + PR² = 2 PS² + 2 SR² [Apollonius theorem] ∴ 11² + 17² =... 1
- Identify, with reason, which of the following are Pythagorean triplets. i. (3,5,4) Here, 5² = 25 3² + 4² = 9 + 16 = 25 ∴ 5² = 3² + 4² The square of the largest number is equal to the sum of the squares of the oth... 1
- In the given figure, if LK = 6√3 find MK, ML, KN, MN and the perimeter of MNKL Solution:: In triangle space LKM , tan30^∘ =MLover LK ⇒ ML=6√( 3 ) × 1 / √( 3 ) =6 cos 30 ^(°) = LK / MK ⇒ MK=dfrac LK cos 30 ^(°) = 6√( 3 )... 1
- Walls of two buildings on either side of a street are parallel to each other. A ladder 5.8 m long is placed Solution:: Correct answer is 8.2 m Video solution https://youtu.be/WmtS_3V0VKQ 1
- A ladder 25m long just reaches the top of a building 24m Given: length of ladder= 25 m building height=24 m By pythagoras theorem , x²=25² -24² =625-576 x²=49 x= 7 Hence the answer is 7 m https://y... 1
- Find the diagonal of a rectangle whose lengths of sides is 8cm and 15cm. The length of diagonal is 17 cm 1