The lengths of the sides of the triangle are proportional to the numbers 4, 5, 8.

| September 1, 2021 | education

The lengths of the sides of the triangle are proportional to the numbers 4, 5, 8. Find the difference between the large and smaller sides of this triangle if its perimeter is 68cm.

The sides of the triangle are proportional to the numbers 4, 5 and 8, let us denote the coefficient of proportionality of the lengths of the triangle by the letter k.

Hence, the sides of the triangle are equal: 4k, 5k and 8k.

Since the perimeter of the triangle is 68 cm, we make the equation:

4k + 5k + 8k = 68.

17k = 68.

k = 68: 17.

k = 4.

From here we find the lengths of the sides of the triangle:

4k = 4 * 4 = 16 (cm),

5k = 5 * 4 = 20 (cm),

8k = 8 * 4 = 32 (cm).

The large side is 32 cm long, and the smaller one is 16 cm. Let’s calculate the difference between them:

32 – 16 = 16 (cm).

Answer: 16 cm.



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