Median Property

Q.

In a triangle ABC, median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram.

Q. If the length of a median of an equilateral triangle is x cm, then its area is

(a) x²

(b) $\frac{\sqrt{3}}{2}{x}^2$

(c) $\frac{x^2}{\sqrt{3}}$

(d) $\frac{x^2}{2}$

Q. ABCD is a parallelogram and L is the mid point of CD. If Ar (ABCL) = 72 cm${}^2$, then find Ar (ADC).

1. 72 cm${}^2$
2. 144 cm${}^2$
3. 48 cm${}^2$
4. 36 cm${}^2$

Q.

What is the area of $△ABC$ (in square cm) if AD is the median and area $△ADB$= 18 square cm?

1. 36 square cm

2. 12 square cm

3. 9 square cm

4. 18 square cm

Q.

In a given figure, BE is a median of $△ABD$. If the area of parallelogram ABCD is $24c{m}^2$. Then the area of $△ABE$ is:

1. $6c{m}^2$

2. $8c{m}^2$

3. $12c{m}^2$

4. $10c{m}^2$

Q. In triangle ABC, D and E are points on BC such that CD = DE = EB. Find the ratio of areas of triangle ADE and triangle ABC.

1. $\frac{1}{3}$
2. $\frac{1}{4}$
3. $\frac{3}{1}$
4. $\frac{2}{3}$

Q.

AD is median of triangle ABC and DE is median of triangle ABD. The ratio of area triangle BED : area triangle ABC

1. 1 : 2

2. 1 : 3

3. 1 : 8

4. 1 : 4

Q.
From the given figure match the following.

1. $\frac{AB}{BC}$
2. $\frac{AB}{AC}$
3. $\frac{BC}{AC}$

Q.

In a given figure, BE is a median of $△ABD$ and the area of parallelogram ABCD is $24c{m}^2$. Find the area of $△ABE$.

Q. (i) In a given figure, BE is a median of $△$ ABD. If the area of parallelogram ABCD is 24 cm${}^2.$ Then the area of $△$ BDE is:

(ii) In the above diagram if AD = 12 cm then find the value of AE.

Q.

AD is the median of △ ABC and DE is the median of △ ABD. If area of △ BED : area of △ ABC =_____.

1. $1:4$

2. $1:1$

3. $1:2$

4. $4:1$

Q. In figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar (ABC) = ar (ABD).

Q.

AD is the median of △ ABC. Area of △ABC : △ADB = ____.

1. $1:2$

2. $1:1$

3. $1:3$

4. $2:1$

Q.

AD is the median of △ ABC. If area of △ ADB = 22.5 sq cm, then the area of △ABC = ____ sq cm.

1. 22.5

2. 11.25

3. 45

4. 50

Q.

If AD is median of ΔABC and P is a point on AC such that ar(ΔADP) : ar(ΔABD) = 2 : 3, then ar(ΔPDC) : ar(ΔABC) is ______ .

1. 3 : 5
2. 2 : 5
3. 1 : 5
4. 1 : 6

Q.

AD is the median of △ ABC. If area of △ ADB = 22.5 sq cm, then the area of △ADC = ____ sq cm.

1. 11.25

2. 22.5

3. 45

4. 50

Q.

AD is the median of △ ABC and DE is the median of △ ABD. If area of △ BED = 2.5 sq cm, then the area of △ ABC = ____ sq cm.

1. 2.5

2. 5

3. 7.5

4. 10

Q.

A man of height y is standing between two buildings with heights x and z respectively as shown in the figure. Then, which of the following statements is true about the relation of the heights?

1. $\frac{1}{x}=\frac{1}{y}=\frac{1}{z}$

2. $x=y=z$

3. $\frac{1}{x}=\frac{1}{y}+\frac{1}{z}$

4. $\frac{1}{x}+\frac{1}{z}=\frac{1}{y}$

Q.

AD is the median of triangle ABC. The ratio of area of ABD : area of ACD is _______.

1. 1 : 2

2. 2 : 1

3. 1 : 3

4. 1 : 1

Q. The vertex $A$ of $△ABC$ is joined to point $D$ on the side $BC$. The midpoint of $AD$ is $E$. Prove that $ar\left(△BEC\right)=\frac{1}{2}ar\left(△ABC\right)$.

Q. If the length of a median of an equilateral triangle is x cm, then its area is

(a) x²

(b)

(c)

(d)