Question

State whether segments of the given lengths can be side of a right angle triangle.

a=7, b=24, and C=25.
Show working to support your answer. *
2 Points

Answer 1

Given:

In a triangle,

`a=7,b=24,c=25`

To find:

Whether the given segments are the sides of a right triangle or not.

Solution:

In a right triangle the square of largest side is equal to the sum of squares of two smaller side.

`c^2=a^2+b^2` (Pythagoras theorem)

Three sides are
`a=7,b=24,c=25`. Here, 25 is the largest side.

`25^2=625`

Now, the sum of squares of two smaller sides is:

`(7)^2+(24)^2=49+576`

`(7)^2+(24)^2=625`

`(7)^2+(24)^2=25^2`

Since the sum of squares of two smaller side is equal to the square of largest side, therefore the given segments are the sides of a right triangle.