Question

ABC is a triangle such that AB: BC: CA = 3:5 : 6 and semi-perimeter of the triangle is 28 cm. If BQ is a median of the triangle, then
find the length of BQ
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Answer 1

Answer:

semi-perimeter of triangle=28cm

therefore, perimeter of triangle = 56cm

3x+5x+6x= 56

14x=56

x=4

therefore,

AB=3x=3(4) =12

BC=5x=5(4) =20

CA=6x=6(4) =24

here, Q with divide AC into two equal parts,

CQ=1/2 AC

CQ=1/2(24)

CQ=12

takingBQC, where Q is a right angle

By Pythagoras theorem,

BC²=BQ²+CQ²

20²=BQ²+12²

400= BQ²+144

400-144=BQ²

256=BQ²

√256=BQ

16=BQ

therefore, BQ(median) = 16cm