Question
Find the length of the altitude of triangle PQR.
- 6.9
- 48
- 24
- 0
Hint:
We are given a right-angled triangle PQR. An altitude is drawn from the vertex having the right angle. The altitude is RS. It divides the base of the triangle into two parts, QS and PS. The values of QS and PS are given. We are asked to find the value of the altitude. To solve this question, we will use the properties of a right-angled triangle.
The correct answer is: 6.9
From the figure, we can write the values of lengths and angles.
Length of QS = 4
Length of PS = 12
Angle PRQ = 90°
Let the value of altitude be “a”.
Due to the altitude, two right-angled triangles are formed.
There is a theorem for altitude drawn from the right angle of a right-angled triangle. It states that, “When altitude is drawn from a right angle, two similar triangles are formed. They are similar to each other. They are also similar to the parent triangle”.
Therefore, the length of the altitude is 6.9.
To solve such questions, we should know the properties of right-angled triangles and similar triangles. Similar triangles have different sizes, but are of same shape. Their sides are in different proportion, but their angles are same. As a shortcut, we can just remember the last step of the above expression.
Related Questions to study
Find the value of y.
For such questions, we should know the properties of right-angled triangle. We should know the trignometric ratios. The values of different sines and cosines should be known.
Find the value of y.
For such questions, we should know the properties of right-angled triangle. We should know the trignometric ratios. The values of different sines and cosines should be known.
A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.
For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem. Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.
A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.
For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem. Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.
