The Altitude on Hypotenuse Theorem

Q.

Question 122

In the given figure, $\Delta AEC$ is right angled at E, B is a point on EC, BD is the altitude of $\Delta ABC$, AC = 25 cm BC = 7 cm and AE = 15 cm. Find the area of $\Delta ABC$ and the length of DB.

Q.

Which of the following combination of sides of a triangle represents a right angled triangle?

1. 9 cm, 12 cm and 15 cm

2. 5 cm, 9 cm and 10 cm

3. 8 cm, 12 cm and 16 cm

4. 4 cm, 6 cm and 8 cm

Q.
If RS is the altitude drawn to the hypotenuse of the right-angled triangle as shown in the above figure, then which of the following are true?

1. $h^2=xy$
2. $h^2=\frac{x}{y}$
3. $△PRQ\sim △PSR$
4. $p^2=yr$

Q.

In $△$ABC, $\angle B$ is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then $AD.DC=$

1. $B{D}^2$

2. $BE.BC$

3. $AB.BC$

4. $BD.DC$

Q. Which of the following is the assumption taken in the converse of Pythagorean theorem?

1. Square of the longest side of the triangle = square of sum of other two sides
2. square of the longest side of the triangle = sum of squares of other two sides
3. Square of the longest side of the triangle = difference of squares of other two sides
4. square of the longest side of the triangle = square of difference of other two sides

Q.

In $△ABC$, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then $AD\times DC$ = ?

1. $B{D}^2$

2. $BE\times BC$

3. $AB\times BC$

4. $BD\times DC$

Q. In a right triangle $\Delta ABC$ with right angle at B, BD is a perpendicular drawn to the hypotenuse AC. Which of the following statements are true?

1. $\Delta ADB$ ~ $\Delta ABC$
2. $\Delta ADB$ ~ $\Delta BDC$
3. $\Delta ABC$ ~ $\Delta BDC$
4. $\Delta ABD$ ~ $\Delta ABC$

Q. $△ABC$ is right angled at B and the perpendicular drawn from B to the opposite side AC bisects it at D. If AD = DC = 5 cm, then find the length of BD.

1. 5 cm
2. 10 cm
3. 25 cm
4. 12.5 cm

Q. In a right angle triangle $\Delta ABC$, a perpendicular BD is drawn on to the largest side from the vertex B. Which of the following does NOT give the ratios of the areas of $\Delta ABD$ and $\Delta BCD$ ?

1. ${\left(\frac{AB}{AC}\right)}^2$
2. ${\left(\frac{AD}{BD}\right)}^2$
3. ${\left(\frac{BD}{DC}\right)}^2$
4. ${\left(\frac{AB}{BC}\right)}^2$

Q. In a right triangle $\Delta ABC$ with right angle at B, a perpendicular BD is drawn from B to the hypotenuse. If AC = 2AB, find the area of $\Delta ADB$.
Given: Area of $\Delta ABC$ = 5 sq units

1. 0.5 sq. unit
2. 1 sq. unit
3. 1.25 sq. unit
4. 5 sq. unit

Q.

In a right triangle $△$ ABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. Which of the following statements are true?

1. $△ADB\sim △ABC$

2. $△ADB\sim △BDC$

3. $△ABC\sim △BDC$

4. None of these

Q. $△ABC$ is right angled at B and the perpendicular drawn from B to the opposite side AC bisects it at D. If AD = DC = 5 cm, then find the length of BD.

1. 5 cm
2. 10 cm
3. 12.5 cm
4. 25 cm