Advertisements
Advertisements
Question
Triangles ABC and DEF are similar.
If AC = 19 cm and DF = 8 cm, find the ratio between the area of two triangles.
Solution
In ΔABC and ΔDEF, AC = 19 cm, DF = 8 cm.
Since, `"area (Δ ABC)"/"area (Δ DEF)" = "AC"^2/"DF"^2 = (19)^2/(8)^2 = (361)/(64)`
Hence, the required ratio is 361: 64.
APPEARS IN
RELATED QUESTIONS
In quadrilateral ABCD, diagonals AC and BD intersect at point E such that
AE : EC = BE : ED. Show that: ABCD is a trapezium.
In the given figure, AD = AE and AD2 = BD × EC. Prove that: triangles ABD and CAE are similar.
In ΔABC, angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that: CB : BA = CP : PA
Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting diagonal AC in L and AD produced in E. Prove that: EL = 2BL.
Triangle ABC is similar to triangle PQR. If AD and PM are altitudes of the two triangles, prove that : `(AB)/(PQ) = (AD)/(PM)`.
Triangles ABC and DEF are similar.
If area (ΔABC) = 36 cm2, area (ΔDEF) = 64 cm2 and DE = 6.2 cm, find AB.
Two isosceles triangle have equal vertical angles and their areas are in the ratio of 36 : 25. Find the ratio between their corresponding heights.
In ΔABC, and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.
In the adjoining figure ABC is a right angle triangle with ∠BAC = 90°, and AD ⊥ BC.
(i) Prove ΔADB ∼ ΔCDA.
(ii) If BD = 18 cm, CD = 8 cm find AD.
(iii) Find the ratio of the area of ΔADB is to area of ΔCDA.
On a map drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = 90°.
Calculate:
- the actual lengths of AB and BC in km.
- the area of the plot in sq. km.
