please please help

Question

Answer 1

(1)

Step 1:

The sides of the triangle are and .

Draw a triangle with sides and .

Step 2:

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

Find whether the triangle is a right angle triangle or not.

For a right angle triangle, Pythagoras theorem:.

.

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

Solution:

The sides of the triangle does not form a right triangle.

Answer 2

(2)

Jamil said the sides of the triangle are and form a right angle triangle.

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

Find whether the triangle is a right angle triangle or not.

For a right angle triangle, Pythagoras theorem:.

.

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

Yes; Jamil is right.

Answer 3

(3)

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

Observe the diagram:

The two timbers of the flower bed are long each.

For a right angle triangle, Pythagoras theorem:.

Substitute and in .

.

The required length of the third timber is  .

Petra has long timber.

Therefore, the long timber is not enough to form a right angle triangle.

Answer 4

(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 other side of the rectangle as .

.

The other side of the rectangle is .

Answer 5

(5)

The length of the ladder is .

The distance between wall and foot of the ladder is .

Let be the height of the ladder from the bottom of the vertical wall.

Draw the related diagram:

For a right angle triangle, Pythagoras theorem:.

.

The height of the ladder from the bottom of the vertical wall is .