Q12 of 186 Page 229

In the given figure and DE : BC = 3: 5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.

It is given that DE || BC


∴∠ ADE = ∠ ABC (Corresponding angles)


∠ AED = ∠ ACB (Corresponding angles)


So, by AA similarity criterion ΔADE ~ ΔABC


We know that if two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.





Hence, proved.


More from this chapter

All 186 →
10

In the given figure, DE || BC. If DE = 3 cm, BC = 6 cm and ar (ΔADE) = 15 cm2, find the area of ΔABC.

 11

ΔABC is right-angled at A and AD ⊥ BC. If BC = 13 cm and AC = 5 cm, find the ratio of the areas of ΔABC and ΔADC.

 13

In ΔABC, D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.

 1

The sides of certain triangles are given below. Determine which of them are right triangles.

(i) 9 cm, 16 cm, 18 cm


(ii) 7 cm, 27 cm, 25 cm


(iii) 1.4 cm, 4.8 cm, 5 cm


(iv) 1.6 cm, 3.8 cm, 4 cm


(v) (a - 1) cm, 2 √a cm, (a + 1) cm