In the give figure, ABC is a triangle with ∠EDB = ∠ACB. Prove that ΔABC ~ ΔEBD. If BE =6 cm, EC = 4cm, BD = 5cm and area of ΔBED = 9 cm2. Calculate the:
(i) length of AB]
(ii) area of Δ ABC
The following figure shows a triangle ABC in which AD and BE are perpendiculars to BC and AC respectively.
(i) ΔADC ~ ΔBEC
(ii) CA × CE = CB × CD
(iii) ΔABC ~ ΔDEC
(iv) CD × AB = CA × DE
In ΔABC, AP : PB = 2 : 3. PO is parallel to BC and is extended to Q so that CQ is parallel to BA.
(i) area ΔAPO : area Δ ABC.
(ii) area ΔAPO : area Δ CQO.
Two isosceles triangles have equal vertical angles. Show that the triangles are similar.If the ratio between the areas of these two triangles is 16 : 25, find the ratio between their corresponding altitudes.
A triangle ABC with AB = 3 cm, BC = 6 cm and AC = 4 cm is enlarged to ΔDEF such that the longest side of ΔDEF = 9 cm. Find the scale factor and hence, the lengths of the other sides of ΔDEF.
The dimensions of the model of a multistoreyed building are 1 m by 60 cm by 1.20 m. if the scale factor is 1 : 50, find the actual dimensions of the building.
(i) the floor area of a room of the building, if the floor area of the corresponding room in the model is 50 sq. cm
(ii) the space (volume) inside a room of the model, if the space inside the corresponding room of the building is `90 m^3`