Use the following figure to find the values of x and y .

Figure PQR represents a triangular floor such that PQ =QR= 2 cm and angle PQR is 90 . Find PR , correct to two decimal places.

In the following figure, AP is perpendicular to BC , AB= 13cm, BP = 5 cm and AC =.15 cm.

Calculate the lengths of AP and CP .

A rectangular frame is made of wooden bars. The diagonal of the frame is 25 cm long and its width is 15 cm. Find the length of the frame.

20. Which of the following triples fits to Pythagoras theorem?

(a) (33, 56, 65)

(b) (15, 30, 35)

.  Find the distance PR in the following figure if the lines PR and RQ are perpendicular.

SECTION B

21. The area of a right-angled triangle is 50cm². If one of its angles is 45°, calculate the lengths of the sides and the hypotenuse of the triangle.

 if   and angle ABD =  Calculate the length

In the following figure, PQ=17 cm, QS =15 cm, RS= 6 cm and PR = x. Find the value of x

The angle of elevation of the top of a vertical building from a point on the ground is 25^°. The point on the ground is 80 m away from the base of the building. By sketching a diagram representing this information, calculate the height of the building.Write the answer correct to one decimal place.

A 4m ladder rests against a vertical wall with its foot 2m from the wall. How far up the wall does the ladder reach? Give your answer in two decimal places.

Use the quadratic formula to solve x² + 4x ? 12 = 0

A ladder leans against a wall. If the ladder reaches 12m up the wall and its foot is 9m from the base of the wall, find the length of the ladder.

A ladder reaches the top of a wall 18m high when the other end on the ground is 8m from the wall. Find the length of the ladder.

Given the right angled triangle above whose sides are measured in centimeter determine:

1. the value of x
2. the area of the triangle (6 marks)

A photograph which has a diagonal of 7.8 cm long is to be fitted in a frame. Show whether the photograph will fit in the frame measuring 6 cm long and 5 cm wide. 

The sides of an equilateral triangle ABC are 10cm each. Find the length marked AD in surd form.

Find the perimeter of a right angled triangle whose base is  cm and height is cm

A ladder on the ground leans against a vertical wall whose height is 5 metres. The ground distance between the ladder and the wall is 12 metres.

(i) Draw a diagram to represent this information. 

(ii) Using the diagram in part (i), find the length of the ladder.