Mathematics
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC.
(i) Prove that △ADE ~ △ACB.
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of △ADE : area of quadrilateral BCED.
Related Questions
Two isosceles triangles have equal vertical angles and their areas are in the ratio 7 : 16. Find the ratio of their corresponding heights.
In the given figure,
∠ PQR = ∠ PST = 90°, PQ = 5 cm and PS = 2 cm.(i) Prove that △PQR ~ △PST.
(ii) Find area of △PQR : area of quadrilateral SRQT.
In the figure (ii) given below, ∠ABC = ∠DAC and AB = 8 cm, AC = 4 cm, AD = 5 cm.
(i) Prove that △ACD is similar to △BCA.
(ii) Find BC and CD.
(iii) Find area of △ACD : area of △ABC.
On a map drawn to a scale of 1 : 250000, a triangular plot of land has the following measurements :
AB = 3 cm, BC = 4 cm and ∠ABC = 90°. Calculate :
(i) the actual length of AB in km.
(ii) the area of the plot in sq. km.