If the altitude of an isosceles right triangle has a length of x units, what is the length of one leg of the large right triangl
2 answers:
To solve the problem we must know about isosceles right triangle and the Pythagorean Theorem.
<h2>Isosceles Triangle</h2>A triangle with two sides of equal length and the corresponding angles of equal measurement is known as Isosceles Triangle.
<h2>Right Triangle</h2>A tringle with a 90° angle is known as a right-angled triangle.
The length of one leg of the large right triangle in terms of x is x√2.
<h2>Explanation</h2>Given to us
- If the altitude of an isosceles right triangle has a length of x units,
As it is given to us that the triangle is a right angle triangle the two sides of the triangle will be equal to each other.
therefore, AB = BC
Also, given that the altitude of the triangle is equal to x. therefore,
AB = x
AB = BC = x,
<h3>What is the largest side of the right triangle?</h3>We know that in a right-angled triangle the longest side of the triangle is the hypotenuse, which is always opposite to the 90° angle.
<h3>In ΔABC,</h3>AC is the hypotenuse,
Using Pythagoras theorem,
AC² = AB² + BC²
thus, the value of hypotenuse is x√2.
Hence, the length of one leg of the large right triangle in terms of x is x√2.
Learn more about Hypotenuse:
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