Question

The dimensions of a triangle are in the ratio of 2: 4: 5 and its perimeter is 66 m. The largest side of the triangle is _____ m.

• A. 12
• B. 24
• C. 30
• D. 36

Answer 1

The correct option is C 30

Given, the dimensions of the triangle are in the ratio of 2: 4: 5.
Let the sides of the triangle be $2x,4x$ and $5x.$
Perimeter of the triangle = $2x+4x+5x=11x$
Given that the perimeter of the triangle is 66 m.
$\Rightarrow 66=11x$
Dividing both sides of the equation by 6, we get
$x=\frac{66}{11}=6\text{m}.$
Hence, the dimensions of the triangle are
$2x=2\times 6\text{m}=12\text{m}$
$4x=4\times 6\text{m}=24\text{m}$ and
$5x=5\times 6\text{m}=30\text{m}.$
So, the largest side of the triangle is 30 m.