Advertisements
Advertisements
प्रश्न
If AD is a median of a triangle ABC, then prove that triangles ADB and ADC are equal in
area. If G is the mid-point of median AD, prove that ar (Δ BGC) = 2 ar (Δ AGC).
Advertisements
उत्तर
Draw AM ⊥ BC
Since, AD is the median of ΔABC
∴ BD = DC
⇒ BD = AM = DC × AM
⇒ ` 1/2 (BD xx AM ) = 1/2 ( DC xx AM)`
⇒ ar (Δ ABC) = ar (Δ ACD) ........ (1)
In ΔBGC , GDis the median
∴ ar (BGD) = area (OGD) ......... (2)
In ΔACD , CG is the median
∴ area (AGC) = area (Δ CGD) ......... (3)
From (1) and (2) , we have
Area (ΔBGD) = ar (Δ AGC)
But, ar (ΔBGC) = 2ar (BGD)
∴ ar (BGC ) = 2ar (Δ AGC)
APPEARS IN
संबंधित प्रश्न
In the given figure, ABCD is a rectangle with sides AB = 10 cm and AD = 5 cm. Find the area of ΔEFG.
Two parallelograms are on the same base and between the same parallels. The ratio of their areas is
The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is ______.
ABCD is a trapezium in which AB || DC. If ar (ΔABD) = 24 cm2 and AB = 8 cm, then height of ΔABC is
Find the area of a rectangle whose length = 3.6 m breadth = 90 cm
Find the area of a rectangle whose length = 24 cm breadth =180 mm
The side of a square field is 16 m. What will be increase in its area, if each of its sides is increased by 4 m?
Nasreena is a farmer who wants to divide her land equally among her three children — Chumki, Jhumri, and Imran. She wants to divide the land so that each piece of land has one tree. Her land looks like this.
- Can you divide the land equally? Show how you will divide it. Remember each person has to get a tree. Colour each person’s piece of land differently.
An engineer who plans to build a compound wall on all sides of a house must find the area of the compound.
Find the area of the following figure by counting squares:
