Question

Two right triangles are shown. First, find the missing leg of the triangle on the right. Then you have two lengths to use to find the missing hypotenuse of the triangle on the left.

Answer 1

x = 30m

Explanation:

GIVEN :-

There are 2 right-angled triangles.

In the triangle on the right side ,

• Hypotenuse = 26m
• Base = 10m

In the triangle on the left side ,

• Base = 18m

TO FIND :-

• Length of the common perpendicular to both triangles.
• Length of the hypotenuse of the triangle on the left side.

FACTS TO KNOW BEFORE SOLVING :-

• 
  `Hypotenuse = √(Base^2 + Perpendicular^2)`.
• 
  `Perpendicular = √(Hypotenuse^2 - Base^2)`

SOLUTION :-

In the triangle on the right side ,

`Perpendicular = √(26^2 - 10^2) = √(676 - 100) = √(576) = 24m`

⇒ Perpendicular of the triangle on right side = Perpendicular of the triangle on left side.

In the triangle on the left side ,

`Hypotenuse = √(24^2 + 18^2) = √(576 + 324) = √(900) = 30m`

∴ x = 30m