Question

Triangle ABC is a right angled at B. If AB is 9cm,AC is 15cm and D andE are the mid-point of the side AB and AC respectively,then calculate
(i)the length of BC
(ii)the area of triangle ADE

Answer 1

AB= 9 cm ; AC = 15 cm;
ABC is a right angle triangle.
using Pythagoras theorem,
AC² = AB² + BC²
i) BC² = AC² - AB²
BC = √(15² - 9²) = 12 cm
ii) D & E are the mid point of the lines AB & AC respectively.
therefore, AD = 9/2 = 4.5 cm
AE = 15/2 = 7.5 cm
now, ADE also a right angle triangle.
using Pythagoras theorem,
AE² = AD² + DE²
or, DE² = AE² - AD²
or, DE = √(7.5² - 4.5²) = 6 cm.