Advertisements
Advertisements
प्रश्न
In ΔABC, DE || BC (as shown in the figure), If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is ______.
विकल्प
6 cm
7.5 cm
9 cm
5.7 cm
उत्तर
In ΔABC, DE || BC (as shown in the figure), If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is 7.5 cm.
Explanation:
Given: AD = 4 cm, AB = 9 cm, and AC = 13.5 cm
Using the properties of similar triangles, when DE || BC, triangles ADE and ABC are similar.
From the similarity of the triangles:
`(AD)/(AB) = (AE)/(AC)`
Now we can express AE in terms of AC, since AE + EC = AC:
`4/9 = (AE)/13.5`
AE = `4/9 xx 13.5`
AE = 6
Now EC will be:
EC = AC − AE
EC = 13.5 − 6
EC = 7.5
APPEARS IN
संबंधित प्रश्न
In figure, `\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}` and AB = 5 cm. Find the value of DC.
In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
In the following figure, seg DH ⊥ seg EF and seg GK ⊥ seg EF. If DH = 18 cm, GK = 30 cm and `A(triangle DEF) = 450 cm^2`, then find:
1) EF
2) `A(triangle GFE)`
3) `A(square DFGE)`
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
- ΔADE ∼ ΔACB.
- If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
- Find, area of ΔADE : area of quadrilateral BCED.
The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, what is the corresponding side of the other triangle?
State, true or false:
Two isosceles-right triangles are similar.
Area of two similar triangles are 98 sq. cm and 128 sq. cm. Find the ratio between the lengths of their corresponding sides.
ABC is a triangle. PQ is a line segment intersecting AB in P and AC in Q such that PQ || BC and divides triangle ABC into two parts equal in area. Find the value of ratio BP : AB.
On a map, drawn to a scale of 1 : 250000, a triangular plot PQR of land has the following measurements :
PQ = 3cm, QR = 4 cm and angles PQR = 90°
(i) the actual lengths of QR and PR in kilometer.
(ii) the actual area of the plot in sq . km.
P and Q are points on the sides AB and AC respectively of a ΔABC. If AP = 2cm, PB = 4cm, AQ = 3cm and QC = 6cm, show that BC = 3PQ.
Two chords AB and CD of a circle intersect at a point P outside the circle.
Prove that: (i) Δ PAC ~ Δ PDB (ii) PA. PB = PC.PD
In a right triangle ABC, right angled at B, D is a point on hypotenuse such that BD ⊥ AC , if DP ⊥ AB and DQ ⊥ BC then prove that
`(a) DQ^2 Dp.QC (b) DP ^2 DQ.AP 2 `
If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false?
In Δ ABC , DE is parallel to BC and `"AD"/"DB" = 2/7` IF AC = 5 .6 , find AE.
In figure , DEF is a right -angled triangle with ∠ E = 90 °.FE is produced to G and GH is drawn perpendicular to DE = 8 cm , DH = 8 cm ,DH = 6 cm and HF = 4 cm , find `("Ar" triangle "DEF")/("Ar" triangle "GHF")`
D and E are points on the sides AB and AC respectively of Δ ABC such that AB=5.6cm, AD= 1.4cm, AC=7 .2cm and AE = 1.5 cm, show that DE is parallel to BC
The length of a river in a map is 54cm. if lcm on the map represents 12500m on land, find the length of the river.
In ΔABC, point D divides AB in the ratio 5:7, Find: `"AD"/"AB"`
AM and DN are the altitudes of two similar triangles ABC and DEF. Prove that: AM : DN = AB : DE.
In a right-angled triangle ABC, ∠B = 90°, P and Q are the points on the sides AB and AC such as PQBC, AB = 8 cm, AQ = 6 cm and PA:AB = 1:3. Find the lengths of AC and BC.
The areas of two similar triangles are 169cm2 and 121cm2 respectively. If one side of the larger triangle is 26cm, find the length of the corresponding side of the smaller triangle.
In ΔABC, AB = 8cm, AC = 10cm and ∠B = 90°. P and Q are the points on the sides AB and AC respectively such that PQ = 3cm ad ∠PQA = 90. Find: The area of ΔAQP.
A plot of land of area 20km2 is represented on the map with a scale factor of 1:200000. Find: The ground area in km2 that is represented by 2cm2 on the map.
A model of cargo tuck is made to a scale of 1:40. The length of the model is 15cm. Calculate: The base area of the truck, if the base area of the model is 30m2
In the given figure, UB || AT and CU ≡ CB Prove that ΔCUB ~ ΔCAT and hence ΔCAT is isosceles.
If in triangles PQR and XYZ, `"PQ"/"XY" = "QR"/"ZX"` then they will be similar if
ΔPQR ~ ΔSUV. Write pairs of congruent angles
In given fig., quadrilateral PQRS, side PQ || side SR, AR = 5 AP, then prove that, SR = 5PQ
Areas of two similar triangles are equal then prove that triangles are congruent
