Answer:
√190
Explanation:
In the figure , there are 2 right angled triangles with a common perpendicular & both the triangles combine to form a new right angled triangle.
Let the triangle with 9 as base be T¹ & Let the triangle with base 10 be T². Let the triangle formed by T¹ & T² be T³.
In T² ,
Hypotenuse = y
Base = 10
According to Pythagorean Theorem ,
(Hypotenuse)² = (Base)² + (Perpendicular)²
Hence, (Perpendicular)² =

In T¹ ,
Perpendicular =
(∵ Both T¹ & T² have common perpendicular)
⇒(Perpendicular)² =

Base = 9
⇒ (Base)² = 9²
Hypotenuse =
Using Pythagorean Theorem ,
(Hypotenuse)² = (Perpendicular)² + (Base)²
⇒ (Hypotenuse)² =
.............................................eqn.2
Now in T³ ,
Base = y
⇒ (Base)² = y²
Perpendicular =
(∵Perpendicular of T³ = Hypotenuse of T²)
⇒ (Perpendicular)² =

Hypotenuse = 9 + 10 = 19
Using Pythagorean Theorem ,
(Hypotenuse)² = (Perpendicular)² + (Base)²
