Question

Срочно!! Помогите)Один із катетів прямокутного трикутника дорівнює 21 см, а другий катет на 7 см менший від гіпотенузи. Знайдіть площу!

Answer 1

По формуле c^2=a^2+b^
то отсюда найдем, что квадрат гипотенузы будет равен
с^2=21*21+14*14=441+196=637
с=sqrt(637) или с=корень из 637

Answer 2

Problem Analysis

We are given a right triangle with one leg measuring 21 cm and the other leg being 7 cm smaller than the hypotenuse. We need to find the area of this triangle.

Solution

To find the area of a right triangle, we can use the formula: Area = (1/2) * base * height.

In this case, the two legs of the triangle are the base and height. Let's denote the base as b, the height as h, and the hypotenuse as c.

We are given that one leg measures 21 cm, so we can set b = 21 cm.

We are also given that the other leg is 7 cm smaller than the hypotenuse, so we can express this as h = c - 7 cm.

To find the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In equation form, this is: c^2 = b^2 + h^2.

Substituting the values we have, we get: c^2 = (21 cm)^2 + (c - 7 cm)^2.

Now we can solve this equation to find the value of c.

Let's calculate the value of c using the given information.

Calculation

Using the equation c^2 = (21 cm)^2 + (c - 7 cm)^2, we can expand and simplify the equation:

c^2 = 441 cm^2 + (c^2 - 14c + 49 cm^2) c^2 - c^2 + 14c = 441 cm^2 + 49 cm^2 14c = 490 cm^2 c = 490 cm^2 / 14 c = 35 cm

Now that we have the value of c, we can calculate the area of the triangle using the formula Area = (1/2) * base * height.

Substituting the values we have, we get: Area = (1/2) * 21 cm * (35 cm - 7 cm).

Calculation

Using the formula Area = (1/2) * 21 cm * (35 cm - 7 cm), we can calculate the area:

Area = (1/2) * 21 cm * 28 cm Area = 294 cm^2

Therefore, the area of the right triangle is 294 cm^2.

I hope this helps! Let me know if you have any further questions.