Advertisements
Advertisements
Question
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
Find, area of ΔADE : area of quadrilateral BCED.
Solution
We need to find the area of ADE and quadrilateral BCED
Area of ΔADE = `1/2 xx AE XX DE = 1/2 xx 4 xx 5/3 = 10/3 cm^3`
Area of quad.BCED = Area of ΔABC Area of ΔADE
` = 1/2 xx BC xx AB - 10/3`
`= 1/2 xx 5 xx 12 - 10/3`
`= 30 - 10/3`
`= 80/3 cm^2`
Thus ratio of areas of ADE to quadrilateral BCED = `(10/3)/(80/3) = 1/8`
APPEARS IN
RELATED QUESTIONS
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 the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm.
- Write all possible pairs of similar triangles.
- Find lengths of ME and DM.
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
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
Triangles ABC and DEF are similar.
If area (ΔABC) = 9 cm2, area (ΔDEF) = 64 cm2 and DE = 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.
Two isosceles triangle have equal vertical angles and their areas are in the ratio of 36 : 25. Find the ratio between their corresponding heights.
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.
In the given figure ΔABC and ΔAMP are right angled at B and M respectively.
Given AC = 10 cm, AP = 15 cm and PM = 12 cm.
(i) Prove ΔABC ∼ Δ AMP.
(ii) Find AB and BC.
