Question 93

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:7 and area of ΔADE is 8 cm sq, what is the area (in sq cm) of quadrilateral BDEC?

Solution

For ADE & ABC are similar , AD:AB = 2:7

for similar triangles

Ratio of sides = $$\sqrt{ \text(ratio of areas)}$$

2:7 = $$\sqrt{ \text(ratio of areas)}$$

4:49 = $$\frac{area of ADE}{area of ABC}$$

4:49 = $$\frac{8}{area of ABC}$$

area of ABC = 98

area of DBCE = area of ABC - area of ADE = 98 - 8 = 90

So the answer is option C.

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