The perimeter of a right angled isosceles triangle is (square root of 2 +1) cm.
Calculate the length of the diagonal of the square which is drawn on
the hypotenuse of that triangle.
Answers
Answer:
√2 cm
Step-by-step explanation:
In isosceles triangle, two sides are equal. In isosceles right triangle, sides other than hypotenuse are equal.
Let the length of each equal side be 'x' and hypotenuse be 'k'.
Perimeter = x + x + k
√2 + 1 = 2x + k ...(1)
Since, this is a right angled triangle as well, we have(using Pythagoras theorem)
⇒ x² + x² = k²
⇒ 2x² = k²
⇒ x = k/√2 .
Substitute this in (1):
⇒ √2 + 1 = 2x + k
⇒ √2 + 1 = 2(k/√2) + k
⇒ √2 + 1 = √2k + k
⇒ √2 + 1 = k(√2 + 1)
⇒ 1 = k
It means, hypotenuse = k = 1 cm
As hypotenuse of the triangle is the side of the square.
Diagonal = side√2
= 1 * √2
= √2 cm
For the explanations Refer the above attachments .
