Question

The lengths of the sides of a triangle are 5 cm, 12 cm and 13 cm. The length of the perpendicular from the opposite vertex to the side whose length is 13 cm is $\frac{m}{13}$. Find the value of $m÷10$.

• A. 6
• B. 60
• C. 5
• D. 13

Answer 1

The correct option is A 6

Here, a = 5, b = 12 and c = 13.
$\therefore s=\frac{1}{2}(a+b+c)=\frac{1}{2}(5+12+13)=15$.
Let A be the area of the given triangle.
Then,
$A=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{15(15-5)(15-12)(15-13)}$
$\Rightarrow A=\sqrt{15\times 10\times 3\times 2}=30c{m}^2$

Let p be the length of the perpendicular from vertex A to the side BC. Then,
$A=\frac{1}{2}\times \left(13\right)\times p$
From (i) and (ii) we get
$\frac{1}{2}\times \left(13\right)\times p=30\Rightarrow p=\frac{60}{13}cm$
Hence $m÷10=60÷10=6$.