Pythagoras’ theorem：练习题

In a right-angled triangle, the hypotenuse is 10 m and one of the shorter sides is 8 m. Find the length of the third side.

A ladder of length 13 m is leaned against a vertical wall. The top of the ladder reaches a point 12 m above the ground. How far is the base of the ladder from the foot of the wall?

A rhombus has diagonals of length 12 cm and 16 cm. Calculate the length of one side of the rhombus.

In a right-angled triangle, the hypotenuse is \(13\) cm and one of the shorter sides is \(5\) cm. Find the length of the third side.

A circle has a radius of 13 cm. A chord in the circle has a length of 24 cm. Calculate the perpendicular distance from the centre of the circle to the chord.

In a right-angled triangle, the hypotenuse is 13 cm and one of the other sides is 12 cm. Find the length of the third side.

Calculate the distance between the points A\((1, 2)\) and B\((5, 5)\) on a coordinate grid.

A point P is 25 cm from the center of a circle. A tangent segment from P to the circle touches the circle at point T and has a length of 24 cm. Calculate the radius of the circle.

A rectangular field has a length of \( 40 \) m and a width of \( 30 \) m.
(a) Calculate the length of the diagonal path that runs from one corner to the opposite corner.
(b) Calculate the total perimeter of the field.

A hiker walks \( 8 \) km due North from point \( P \) to point \( Q \), and then walks \( 15 \) km due East from point \( Q \) to point \( R \).
(a) Calculate the direct distance from point \( P \) to point \( R \).
(b) The hiker then walks directly back to point \( P \) from point \( R \) at a speed of \( 4 \) km/h. Calculate the time taken for this return journey in hours and minutes.