Question

in triangle abc right angled at B and BD perpendicular to AC if ad is equal to 8 cm and CD is equal to 10 cm then ab is equal to​

Answer 1

Given :

• ∠ABC = 90°
• AD = 8
• CD = 10

To find :

• Length of AB

Solution :

• Refer the attached figure.
• BD is perpendicular to AC.

        ∴ ∠ADB = ∠CDB = 90°

• Here, we use the Pythagoras theorem which states that in a right angled triangle, the square of the hypotenuse is equal to the sum of squares of other two sides.

     ∴ AB² = AD² + BD²

     ∴ AB² = 8² + BD²    ....(1)

• Applying Pythagoras theorem in ΔCDB,

        BC² = CD² + BD²

     ∴ BC² = 10² + BD²   ....(2)

• Applying Pythagoras theorem in ΔABC,

        AC² = AB² + BC²

        18² = (8² + BD²) + (10² + BD²)    ....(from (1) and (2))

     ∴ 324 = 164 + 2 BD²

     ∴ 2 BD² = 160

     ∴ BD² = 80    ....(3)

• Substituting (3) in equation (1),

        AB² = 64 + 80

     ∴ AB² = 144

     ∴ AB = 12 units

Answer : The length of AB is 12 units.

Answer 2

hope this helps...thank you