D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD : DB = 2 : 3 and area of ΔABC is 100 sq cm, what is the area (in sq cm) of quadrilateral BDEC?
84
Since \(DE \parallel BC\), \(\triangle ADE \sim \triangle ABC\) with ratio \(\dfrac{AD}{AB}=\dfrac{2}{2+3}=\dfrac{2}{5}\).
By the area ratio of similar triangles:
\[\frac{[\triangle ADE]}{[\triangle ABC]}=\left(\frac{2}{5}\right)^2=\frac{4}{25}\]
\[[\triangle ADE]=100\times\tfrac{4}{25}=16 \text{ sq cm}\]
Therefore \([BDEC]=100-16=\mathbf{84}\) sq cm.
Similar Questions
The bisector of ∠B in ΔABC meets AC at D. If AB = 12 cm, BC = 18 cm and AC = 15 cm, then the length of AD (in cm) is:
What is the length (in cm) of the smallest altitude of the triangle whose sides are 5 cm, 12 cm and 13 cm? (correct to one decimal place)
The perimeter of a semi circle is 25.7 cm. What is its diameter (in cm)? (π = 3.14)
A square has the perimeter equal to the circumference of a circle having radius 7 cm. What is the ratio of the area of the circle to area of the square? (Use π = 22/7)
ABC is an equilateral triangle with side 12 cm. What is the length of the radius of the circle inscribed in it ?
The area of a square shaped field is 1764 m 2. The breadth of a rectangular park is \(\frac{1}{6}\)th of the side of the square field and the length is four times its breadth. What is the cost (in Rs.) of levelling the park at Rs. 30 per m 2?
The area of a circular park is 12474 m 2. There is 3.5 m wide path around the park. What is the area (in m 2) of the path? (Take π = \(\rm \frac{22}{7}\) )
In∆ ABC , ∠A = 88°. If I is the incentre of the triangle, then the measure of ∠BICis:
Chords AB and CD of a circle intersect externally at P. If AB = 7 cm, CD = 1 cm and PD = 5 cm, then the length of PB (in cm) is:
If length of a rectangle is increased to its three times and breadth is decreased to its half, then the ratio of the area of given rectangle to the area of new rectangle is:
Important Questions from Plane Figures
If the area of a square is 625 cm 2, then what is the perimeter of the square?
The area and the perimeter of a sheet of paper are 240 cm 2and 68 cm, respectively. What would be its length and breadth?
One side of rectangular field is 15 meters and one of its diagonals is 17 meters. Then find the area of the field.
The bisector of ∠B in ΔABC meets AC at D. If AB = 12 cm, BC = 18 cm and AC = 15 cm, then the length of AD (in cm) is:
The perimeter and the length of one of the diagonals of a rhombus is 26 cm and 5 cm respectively. Find the length of its other diagonal (in cm).
