# The hypotenuse of a right-angled triangle is 40 cm, and the legs are in the ratio 3: 4.

August 18, 2021 | education

| **The hypotenuse of a right-angled triangle is 40 cm, and the legs are in the ratio 3: 4. Find the perimeter of a triangle if its area is 384cm2?**

According to the condition of the problem, a right-angled triangle is given, the area of which is 384 cm².

It is known that the ratio of his legs is 3: 4.

By designating the larger of them as “x” cm, the smaller one will be equal to “0.75x” cm.

Let’s make an equation based on the area formula *:

S = 1/2 * (a * b);

384 = 1/2 * (x * 0.75x);

384 = 1/2 * (0.75x²);

0.75x² = 768;

x² = 1024;

x = √1024 = 32 cm one of the legs.

Let’s calculate the length of the second one:

32 * 0.75 = 24 cm.

Let’s find what the perimeter of this triangle is equal to:

P = 40 + 32 + 24 = 96 cm.

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