12. ABCisan isosceles triangle right angledat B. Similar triangles ACD

1.	12. ABCisan isosceles triangle right angledat B. Similar triangles ACD and ABFare constructed on sides AC and AB.Find the ratio between the arcas ofAABE and AACD.idea nfa right angicd triangle. Show that the
Answer» Given ΔABC is an isosceles triangle in which ∠B = 90°⇒ AB = BCBy Pythagoras theorem, we have AC^2= AB^2+ BC^2⇒AC^2= AB^2+ AB^2[Since AB = BC]∴ AC^2= 2AB^2→ (1)It is also given that ΔABE ~ ΔACD Recall that ratio of areas of similar triangles is equal to ratio of squares of their corresponding sides Hence ar(ABE)/ar(ACD)=AB^2/AC^2ar(ABE)/ar(ACD)=AB^2/2AB^2 (From1)=1/2The ratio is 1:2

12. ABCisan isosceles triangle right angledat B. Similar triangles ACD and ABFare constructed on sides AC and AB.Find the ratio between the arcas ofAABE and AACD.idea nfa right angicd triangle. Show that the

Answer»

Given ΔABC is an isosceles triangle in which ∠B = 90°⇒ AB = BCBy Pythagoras theorem,

we have AC^2= AB^2+ BC^2⇒AC^2= AB^2+ AB^2[Since AB = BC]∴ AC^2= 2AB^2→ (1)It is also given that ΔABE ~ ΔACD

Recall that ratio of areas of similar triangles is equal to ratio of squares of their corresponding sides

Hence ar(ABE)/ar(ACD)=AB^2/AC^2ar(ABE)/ar(ACD)=AB^2/2AB^2 (From1)=1/2The ratio is 1:2