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In this lesson, we will learn how to use the Pythagorean theorem to find the length of the hypotenuse or a leg of a right triangle and its area.

Q1:

Find π₯ in the right triangle shown.

Q2:

Find the area of the triangle π΄ π΅ πΆ , correct to one decimal place.

Q3:

Given that the triangle π΄ π΅ πΆ is right-angled at π΅ , π΄ π΅ = 1 2 c m , and π΅ πΆ = 5 c m , find the length of π΄ πΆ .

Q4:

Given that the triangle π΄ π΅ πΆ is right-angled at π΅ , π΄ π΅ = 1 2 c m , and π΅ πΆ = 1 6 c m , find the length of π΄ πΆ .

Q5:

Determine the length of the longest side of a right triangle if the lengths of the two other sides are 6 cm and 8 cm.

Q6:

Determine the length of the longest side of a right triangle if the lengths of the two other sides are 32 cm and 60 cm.

Q7:

Determine, to the nearest tenth, the perimeter of a right triangle, given that its hypotenuse is 49 cm and that one of its sides is 26 cm.

Q8:

Given that π΄ π΅ πΆ π· is a square, find the length of π· πΈ .

Q9:

Find the length of the hypotenuse of a right triangle whose leg lengths are 1.

Q10:

Find the length of the hypotenuse of a right triangle whose leg lengths are 3 and 4.

Q11:

Q12:

Q13:

Q14:

Q15:

Q16:

Q17:

Q18:

Q19:

Q20:

π΄ π΅ πΆ is a right-angled triangle at π΅ , where π΄ π΅ = 1 2 6 c m and π΅ πΆ = 7 8 . 4 c m . Find the length of π΄ πΆ .

Q21:

A triangle has vertices at the points π΄ ( 4 , 1 ) , π΅ ( 6 , 2 ) , and πΆ ( 2 , 5 ) .

Work out the lengths of the sides of the triangle. Give your answers as surds in their simplest form.

Is the triangle a right triangle?

Q22:

Q23:

In a right-angled triangle, which of the following is equal to the area of the square that has the hypotenuse as a side?

Q24:

Determine the diagonal length of the rectangle whose length is 48 cm, and width is 20 cm.

Q25:

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