Advertisements
Advertisements
प्रश्न
In the given figure, DE║BC. If DE = 3cm, BC = 6cm and ar(ΔADE) = `15cm^2`, find the area of ΔABC.
उत्तर
It is given that DE || BC
∴ ∠𝐴𝐷𝐸= ∠𝐴𝐵𝐶 (𝐶𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑎𝑛𝑔𝑙𝑒𝑠)
∠𝐴𝐸𝐷= ∠𝐴𝐶𝐵 (𝐶𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑎𝑛𝑔𝑙𝑒𝑠)
By AA similarity, we can conclude that Δ ADE ~ Δ ABC
`(ar(ΔADE))/(ar(ΔABC))=(DE)^2/(BC)^2`
⇒ `15/(ar(ΔABC))=3^2/6^2`
⇒ `ar(ΔABC)=(15xx36)/9`
= `60cm^2`
Hence, area of triangle ABC is `60 cm^2`
APPEARS IN
संबंधित प्रश्न
Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.
E and F are points on the sides PQ and PR, respectively, of a ΔPQR. For the following case, state whether EF || QR:
PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
E and F are points on the sides PQ and PR, respectively, of a ΔPQR. For the following case, state whether EF || QR.
PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
In triangle ABC, DE is parallel to BC; where D and E are the points on AB and AC respectively.
Prove: ∆ADE ~ ∆ABC.
Also, find the length of DE, if AD = 12 cm, BD = 24 cm BC = 8 cm.
In the figure, PQRS is a parallelogram with PQ = 16 cm and QR = 10 cm. L is a point on PR such that RL : LP = 2 : 3. QL produced meets RS at M and PS produced at N.
Find the lengths of PN and RM.
In triangle ABC, AD is perpendicular to side BC and AD2 = BD × DC. Show that angle BAC = 90°.
In the given figure, QR is parallel to AB and DR is parallel to AB and DR is parallel to QB.
Prove that: PQ2 = PD × PA.
In the given figure, ∠1 = ∠2 and `(AC)/(BD)=(CB)/(CE)` Prove that Δ ACB ~ Δ DCE.
State the SAS-similarity criterion
If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false?
In the given figure, A – D – C and B – E – C seg DE || side AB If AD = 5, DC = 3, BC = 6.4 then Find BE.
Figure shows Δ PQR in which ST || QR and SR and QT intersect each other at M. If `"PT"/"TR" = 5/3` find `("Ar" (triangle "MTS"))/("Ar" (triangle "MQR"))`
ABCD and PQRS are similar figures. AB= 12cm, BC=x cm, CD= 15 cm, AD= 10 cm, PQ= 8 cm, QR = 5 cm, RS = m cm and PS = n cm .Find the values of x, m and n.
A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate: the length of LM, if L' M' = 5.4 cm.
In the following figure, point D divides AB in the ratio 3 : 5. Find : `(AD)/(AB)`
In the following figure, point D divides AB in the ratio 3 : 5. Find :
DE = 2.4 cm, find the length of BC.
Find the area of the triangle ABC with the coordinates of A as (1, −4) and the coordinates of the mid-points of sides AB and AC respectively are (2, −1) and (0, −1).
If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:
AB = 10.8cm, BD = 4.5cm, AC = 4.8cm, and AE = 2.8cm
Given is a triangle with sides 3 cm, 5 cm and 6 cm. Find the sides of a triangle which is similar to the given triangle and its shortest side is 4.5 cm.
D and E are points on the sides AB and AC of ΔABC such that DE | | BC and divides ΔABC into two parts, equal in area. Find `"BD"/"AB"`.
Find the scale factor in each of the following and state the type of size transformation:
Model volume = 200cm3, Actual volume = 8cm3
A model of a ship is made to a scale of 1:500. Find: The area other deck o the ship, if the area of the deck of its model is m2
On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The area of the plot in sq km
A vertical stick of length 6 m casts a shadow 400 cm long on the ground and at the same time a tower casts a shadow 28 m long. Using similarity, find the height of the tower
If ∆ABC ~ ∆DEF such that area of ∆ABC is 9 cm2 and the area of ∆DEF is 16 cm2 and BC = 2.1 cm. Find the length of EF.
Observe the figure and complete the following activity
In fig, ∠B = 75°, ∠D = 75°
∠B ≅ [ ______ ] ...[each of 75°]
∠C ≅ ∠C ...[ ______ ]
ΔABC ~ Δ [ ______ ] ...[ ______ similarity test]
ΔABP ~ ΔDEF and A(ΔABP) : A(ΔDEF) = 144:81, then AB : DE = ?
Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”.
If ΔABC ∼ ΔDEF and ∠A = 48°, then ∠D = ______.
Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
Using the above theorem prove that a line through the point of intersection of the diagonals and parallel to the base of the trapezium divides the non-parallel sides in the same ratio.
