Question

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

Answer 1

Answer:

√190

Step-by-step 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 = $\sqrt{y^2 - 100}$   (∵ 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 = $\sqrt{(y^2 - 100) + 9^2}$ (∵Perpendicular of T³ = Hypotenuse of T²)

⇒ (Perpendicular)² = $(\sqrt{(y^2 - 100) + 9^2})^2= (y^2 - 100) + 81 = y^2 - 19$

Hypotenuse = 9 + 10 = 19

Using Pythagorean Theorem ,

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

$=> 19^2 = y^2 - 19 + y^2\\\\=> 2y^2 = 19^2 + 19 = 19(19 + 1) = 19*20\\\\=> y^2 = \frac{19*20}{2} = 19*10 = 190\\ \\=> y =\sqrt{190}$