Question

Given the triangle below, choose True or False for the following: 3 in 5 in 4 in True False A F The triangle is a right triangle. The height of the triangle is 5 inches. The perimeter is 12 inches. The area is 60 square inches. B В G o H D I

Answer 1

In the given triangle we have : Hypotenuse = 5 , Base = 4 in, Height = 3 in

To check the triangle is right angle triangle, Apply the pythagoras Theorem :

`\text{ Hypotenuse}^2=Perpendicular^2+Base^2`

Substitute the each value and simplify :

`\begin{gathered} \text{ Hypotenuse}^2=Perpendicular^2+Base^2 \\ 5^2=3^2+4^2 \\ 25=9+16 \\ 25=25 \end{gathered}`

LHS = RHS

Pythagoras Theorem Verified

Hence the given triangle is right angle triangle.

The hieght of the triangle is 3 in

Perimeter of the triangle is the sum of all sides of the triangle

In the given triangle, perimeter = 3 + 4 + 5

Perimeter of the given triangle = 12 in

Area of triangle is express as the 1/2 Height x Base

Area of the given triangle = 1/2 x 3 x 4

Area of the given triangle = 6 in²

Answer :

The triangle is a right triangle : A

The Height of the triangle is 5 inches : G

The perimeter of triangle is 12 inches : C

The area is 60 square inhces : I