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प्रश्न
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then ar (BDE) = `1/4` ar (ABC).
पर्याय
True
False
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उत्तर
This statement is True.
Explanation:
Given: ΔABC and ΔBDE are two equilateral triangles.
Suppose that each sides of triangle ABC be x.
Similarly, D is the mid-point of BC.
So, each side of triangle BDE is `x/2`.
Now, `(Area(ΔBDE))/(Area(ΔABC)) = (sqrt(3)/4 xx (x/2)^2)/(sqrt(3) / 4 xx x^2)`
= `x^2/(4x^2)`
= `1/4`
Therefore, area (ΔBDE) = `1/4` area (ΔABC).
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संबंधित प्रश्न
Show that the diagonals of a parallelogram divide it into four triangles of equal area.
D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC. Show that
(i) BDEF is a parallelogram.
(ii) ar (DEF) = 1/4ar (ABC)
(iii) ar (BDEF) = 1/2ar (ABC)
In the given figure, AP || BQ || CR. Prove that ar (AQC) = ar (PBR).
In the given figure, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.
In ∆ABC, D is the mid-point of AB and P is any point on BC. If CQ || PD meets AB in Q (Figure), then prove that ar (BPQ) = `1/2` ar (∆ABC).
The medians BE and CF of a triangle ABC intersect at G. Prove that the area of ∆GBC = area of the quadrilateral AFGE.
In the following figure, CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY).
In ∆ABC, if L and M are the points on AB and AC, respectively such that LM || BC. Prove that ar (LOB) = ar (MOC)
If the medians of a ∆ABC intersect at G, show that ar (AGB) = ar (AGC) = ar (BGC) = `1/3` ar (ABC)
In the following figure, X and Y are the mid-points of AC and AB respectively, QP || BC and CYQ and BXP are straight lines. Prove that ar (ABP) = ar (ACQ).
