Advertisements
Advertisements
प्रश्न
In Fig below we have AB || CD || EF. If AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm, calculate the values of x and y.
उत्तर
We have AB || CD || EF. If AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm
In ΔECD and ΔEAB
∠CED = ∠AEB [common]
∠ECD = ∠EAB [corresponding angles]
Then, ΔECD ~ ΔEAB ….(i) [By AA similarity]
`therefore"EC"/"EA"="CD"/"AB"` [Corresponding parts of similar Δ are proportional]
`rArr"EC"/"EA"=x/6` .........(ii)
In ΔACD and ΔAEF
∠CAD = ∠EAF [common]
∠ACD = ∠AEF [corresponding angles]
Then, ΔACD ~ ΔAEF [By AA similarity]
`therefore"AC"/"AE"="CD"/"EF"`
`rArr"AC"/"AE"=x/10` ..........(iii)
Add equations (iii) & (ii)
`therefore"EC"/"EA"+"AC"/"AE"=x/6+x/10`
`rArr"AE"/"AE"=(5x+3x)/30`
`rArr1=(8x)/30`
`rArrx=30/8=3.75` cm
From (i) "DC"/"AB"="ED"/"BE"
`rArr3.75/6=y/(y+4)`
⇒ 6y = 3.75y + 15
⇒ 2.25y = 15
`rArry=15/2.25=6.67` cm
APPEARS IN
संबंधित प्रश्न
A vertical stick 10 cm long casts a shadow 8 cm long. At the same time a shadow 30 m long. Determine the height of the tower.
In the following figure, XY || BC. Find the length of XY.
The sides of certain triangles are given below. Determine which of them right triangles are.
(a – 1) cm, `2sqrta` cm, (a + 1) cm
In the given figure, value of x(in cm) is
In figure, if DE || BC, find the ratio of ar(ADE) and ar(DECB).
In figure, l || m and line segments AB, CD and EF are concurrent at point P. Prove that `(AE)/(BF) = (AC)/(BD) = (CE)/(FD)`.
In ΔABC, AP ⊥ BC, BQ ⊥ AC. If AP = 7, BQ = 8 and BC = 12, then find AC.
If ΔABC ∼ ΔDEF such that ∠A = 92° and ∠B = 40°, then ∠F = ?
Diagonals of a trapezium PQRS intersect each other at the point O, PQ || RS and PQ = 3 RS. Find the ratio of the areas of triangles POQ and ROS.
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ΔPQR show that ΔABC ~ ΔPQR.
