The sides of the triangle are proportional to the numbers 7,5,8. Find the perimeter of the triangle if

| June 21, 2021 | education

The sides of the triangle are proportional to the numbers 7,5,8. Find the perimeter of the triangle if a) the sum of the smallest and largest sides is 39cm b) the difference between the largest and smallest sides is 9cm c) the smallest side is 12cm less from the half-perimeter d) the largest side is less than the sum of the other two 8cm.

the rectangle behind X.

А)

The smallest side is 5 * X.

The largest side is 8 * X.

5 * X + 8 * X = 39.

13 * X = 39.

X = 39/13 = 3.

Then the lengths of the sides of the triangle are equal:

5 * 3 = 15 cm.

7 * 3 = 21 cm.

8 * 3 = 24 cm.

Answer: 15 cm, 21 cm, 24 cm.

B).

The largest side is 8 * X.

8 * X – 5 * X = 9.

3 * X = 9.

X = 9/3 = 3 cm.

Then the lengths of the sides of the triangle are equal:

5 * 3 = 15 cm.

7 * 3 = 21 cm.

8 * 3 = 24 cm.

Answer: 15 cm, 21 cm, 24 cm.

С).

The half-perimeter of a triangle is:

p = (5 * X + 7 * X + 8 * X) / 2 = 10 * X.

Then 10 * X – 5 * X = 12.

5 * X = 12.

X = 2.4 cm.

Then the lengths of the sides of the triangle are equal:

5 * 2.4 = 12 cm.

7 * 2.4 = 16.8 cm.

8 * 2.4 = 19.2 cm.

Answer: 12 cm, 16.8 cm, 19.2 cm.

D).

(5 * X + 7 * X) – 8 * X = 8.

4 * X = 8.

X = 2.

5 * 2 = 10 cm.

7 * 2 = 14 cm.

8 * 2 = 16 cm.

Answer: 10 cm, 14 cm, 16 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.