Question

The sides of a triangle are in the ratio 1: 2: 4. The difference between the longest side

Answer 1

Question:-

The sides of a triangle are in the ratio 1 : 2 : 4. The difference between the longest side and the shortest side is 84 cm. What is the perimeter of the triangle ?

Solution:-

The sides of a triangle are in the ratio 1: 2: 4. (Given)

Let the three sides of a triangle be x, 2x and 4x respectively.

So,

ATQ ,

4x - x = 84

3x = 84

x = $\bf \frac{84}{3}$

x = 28

$\therefore$ Longest side = 4x = 4 × 28 = 112 cm.

Shortest side = x = 28 cm.

And, the other side = 2x = 2 × 28 = 56 cm

Now, we have to find the perimeter of the triangle.

Hence, Perimeter of the triangle = (112 + 56 + 28) cm = 196 cm.

The perimeter of the triangle is 196 cm. [Answer]