Advertisements
Advertisements
प्रश्न
In the given figure ABC is a triangle with ∠EDB = ∠ACB.
(i) Prove that ΔABC ∼ ΔEBD.
(ii) If BE = 6 cm, EC = 4 cm, BD = 5 cm and area of ΔBED = 9 cm2. Calculate the length of AB and area of ΔABC.
उत्तर
(i) In ΔABC and ΔEBD,
∠ACB = ∠EDB ...(given)
∠ABC = ∠EBD ...(common)
∴ ΔABC ∼ ΔEBD
Hence Proved.
(ii) We have, `"AB"/"BE"= "BC"/"BD"`
⇒ AB = `(6 xx 10)/(5) = 12 "cm"`.
(iii) `"Area of ΔABC"/"Area of ΔBED" = ("AB"/"BE")^2`
Area of ΔABC = `(12/16)^2 xx 9 "cm"^2`
= 4 x 9 cm2
= 36 cm2.
APPEARS IN
संबंधित प्रश्न
In the figure, given below, straight lines AB and CD intersect at P; and AC || BD. Prove that: If BD = 2.4 cm, AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and PC.
In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 2CO and BO = 2DO; show that: ΔAOB is similar to ΔCOD.
In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 2CO and BO = 2DO; show that: OA × OD = OB × OC.
In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm. Find lengths of ME and DM.
In the following figure, ABCD to a trapezium with AB || DC. If AB = 9 cm, DC = 18 cm, CF = 13.5 cm, AP = 6 cm and BE = 15 cm, Calculate: AF
In the figure given below, AB ‖ EF ‖ CD. If AB = 22.5 cm, EP = 7.5 cm, PC = 15 cm and DC = 27 cm. Calculate : AC
In the given figure, AB and DE are perpendiculars to BC.
Prove that : ΔABC ~ ΔDEC
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.
Triangles ABC and DEF are similar.
If area (ΔABC) = 9 cm2, area (ΔDEF) = 64 cm2 and BC = 5·1 cm find AB.
Triangles ABC and DEF are similar.
If area (ΔABC) = 36 cm2, area (ΔDEf) = 64 cm2 and DE = 6.2 cm, find AB.
