Question

AD is drawn perpendicular to base BC of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.

Answer 1

Since ABC is an equilateral triangle therefore, all the sides of the triangle are of the same measure and the perpendicular AD will divide BC into two equal parts.

Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.

Here, we consider the ΔABD and applying Pythagoras theorem we get,

AB²  = AD²  + BD²  

AD²  = 10²  - 5²    ......[ Given, BC = 10 cm = AB, BD = `1/2` BC ]

AD²  = 100 - 25

AD²  = 75

AD = 8.7

Therefore, the length of AD is 8.7 cm