Question

The three sides of a triangle are 13 m, 14 m and
15 m. What is the length of the perpendicular
drawn on the longest side?​

Answer 1

ANSWER:

11.204m

Step-by-step explanation:

let the perpendicular be Y

then 15m will be divided in two parts let part with one side 13m be called X then other part will be 15 - X

now by PGT

13^2=Y^2 + X^2

169=Y^2+X^2 ........(1)

now apply PGT in other triangle

14^2=Y^2+(15-X)^2

196=Y^2+225+X^2- 30X ......(2)

now (2) -(1)

196=Y^2+X^2+225-30X-(169=Y^2+X^2)

27=225-30X

27-225=-30X

198=30X

66/10=X

now put the value of X in (1)

169=Y^2+X^2

169=Y^2+(66/10)^2

168-1456/100=Y^2

168-14.56=Y^2

125.54=Y^2

Y=11.204