Question

The perimeter of triangular field is 300 cm and its sides are in the ratio 5 : 12 : 13. Find the length of the perpendicular from the opposite vertex to the side whose length is 130 cm.

• A.
  45 cm
• B.
  34 cm
• C.
  46.15 cm
• D.
  
  87 cm
  
  

Answer 1

The correct option is C

46.15 cm
$a:b:c=5:12:13.5+12+13=30a+b+c=300cm\therefore a=\frac{5}{30}\times 300=50cmb=\frac{12}{30}\times 300=120cmc=\frac{13}{30}\times 300=130cm\therefore s=\frac{a+b+c}{2}=\frac{50+120+130}{2}=150cm\therefore \text{Area of the triangular field}=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{150(150-50)(150-120)(150-130)}=\sqrt{150\times 100\times 30\times 20}=3000c{m}^2...\left(1\right)$

Let the length of the perpendicular from the opposite vertex to the side whose length is 130 cm be h cm. Then, Area of the triangular field

$=\frac{130\times h}{2}=65hc{m}^2...\left(2\right)From\left(1\right)and\left(2\right).65h=3000\Rightarrow h=\frac{3000}{65}=46.15cm$
So, option c is correct.