One of the legs of a straight triangle is 4 cm. Find the hypotenuse and the unknown leg

One of the legs of a straight triangle is 4 cm. Find the hypotenuse and the unknown leg. If it is known that the ratio of the hypotenuse to the second leg is 5: 3

From the condition we know that one of the legs of a right-angled triangle is 4 cm. And it is also known that the hypotenuse refers to the second leg as 5: 3. In order to find the length of the hypotenuse and leg, we apply the Pythagorean theorem.

But let’s start by introducing the similarity coefficient x and writing the length of the hypotenuse as 5x and the length of the leg as 3x.

c ^ 2 = a ^ 2 + b ^ 2.

Substitute the values into the formula and get the equation:

(5x) ^ 2 = 4 ^ 2 + (3x) ^ 2;

25x ^ 2 = 16 + 9x ^ 2;

25x ^ 2 – 9x ^ 2 = 16;

16x ^ 2 = 16;

x ^ 2 = 1;

x = 1.

Now let’s find the length of the hypotenuse and leg:

5 * 1 = 5 cm hypotenuse and 3 * 1 = 3 cm leg length.