Step 1:

The sides of the triangle are and .

Since the measure of the longest side is , let and .

\ \

Step 2:

Find the lengths are right angle triangle or not.

Pythagotus theorem:. \ \

.

Since , segments with these measures cannot form a right triangle.

(2)

Jamil said the numbers The sides of the triangle are and form a triangle. \ \

Since the measure of the longest side is , let and .

Find the lengths are right angle triangle or not.

Pythagotus theorem:. \ \

.

Since , segments with these measures can form a right triangle.

Yes; Jamil is right.

(3)

Petra constructing a flower bed in the shape of right triangle.

Observe the diagram:

The two timbers of the flower bed are .

Pythagotus theorem:.

Substitute and in .

.

The required length of the third timber is  .

Petra has long timber.

Therefore, the long timber is does not enough.

(4)

The diagonal of the rectangle is long.

One side of the rectangle is .

Observe the diagram:

For a right angle triangle, Pythagoras theorem:.

Here , .

Consider tther side of the rectangle is \ \

.

The other side of the rectangle is .

(5)

The length of the ladder is .

The distance between wall and foot of the ladder is .

Consider the height of the wall as .

Draw the related diagram:

For a right angle triangle, Pythagoras theorem:.

.

The height of the wall is .