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.