Question

CAN SONEONE PLEASE HELP ME WITH MY MATH PLEASEEEE!!!!!​

Answer 1

√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 =
`y^2 - 10^2 = y^2 - 100`

In T¹ ,

Perpendicular =
`√(y^2 - 100)` (∵ Both T¹ & T² have common perpendicular)

⇒(Perpendicular)² =
`y^2 - 100`

Base = 9

⇒ (Base)² = 9²

Hypotenuse =

Using Pythagorean Theorem ,

(Hypotenuse)² = (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =
`y^2 - 100 + 9^2` .............................................eqn.2

Now in T³ ,

Base = y

⇒ (Base)² = y²

Perpendicular =
`√((y^2 - 100) + 9^2)` (∵Perpendicular of T³ = Hypotenuse of T²)

⇒ (Perpendicular)² =
`(√((y^2 - 100) + 9^2))^2= (y^2 - 100) + 81 = y^2 - 19`

Hypotenuse = 9 + 10 = 19

Using Pythagorean Theorem ,

(Hypotenuse)² = (Perpendicular)² + (Base)²

`=> 19^2 = y^2 - 19 + y^2\\\\=> 2y^2 = 19^2 + 19 = 19(19 + 1) = 19*20\\\\=> y^2 = (19*20)/(2) = 19*10 = 190\\ \\=> y =√(190)`