Find the legs of an isosceles obtuse triangle, the hypotenuse of which is 40 cm.

| May 17, 2021 | education

Consider an isosceles right-angled triangle, in which the hypotenuse c is equal to 40 cm.According to the conditions for specifying the legs, the legs are equal to each other, the length of each of which is denoted by a
Let us apply the Pythagorean theorem, which for our task is formulated by the equality a² + a² = c² or 2 * a² = c². Substituting in this equality the corresponding value of the hypotenuse c = 40 (omitting the unit of measure centimeter), we have: 2 * a² = 40². We divide both sides of the obtained equality by 2. Then, we get an incomplete quadratic equation a² = 800 with respect to the unknown a.
It is easy to verify that the last equation has the following two different roots: a1 = -√ (800) = -20√ (2) and a2 = 20√ (2).
The sideness of the root a = -20√ (2) is obvious. Therefore, the answer to the task will be: the legs are equal in a = 20√ (2) cm ≈ 28.284 cm.
Answer: The legs are equal to 20√ (2) cm.



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