The perimeter of a right angled isosceles triangle is ( √2 +1) cm. Calculate the length of the diagonal of the square which is drawn on the hypotenuse of that triangle
Answers
Answer:
Length of the diagonal of the square is √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
⇒ x² = k²/2
⇒ x = k/√2 [multiply & divide by √2]
⇒ x = √2 k/2 .
Substitute this in (1):
⇒ √2 + 1 = 2x + k
⇒ √2 + 1 = 2(√2k/2) + k
⇒ √2 + 1 = √2k + k
⇒ √2 + 1 = k(√2 + 1)
⇒ 1 = k
It means, hypotenuse = 1 cm
As hypotenuse is the side of the square, in the square:
⇒ side² + side² = diagonal²
⇒ k² + k² = diagonal²
⇒ 1 + 1 = diagonal²
⇒ √2 = diagonal
For the explanations Refer the above attachments .
