Advertisements
Advertisements
प्रश्न
ΔABC ~ ΔDEF and their areas are respectively `100cm^2` and `49cm2`. If the altitude of ΔABC is 5cm, find the corresponding altitude of ΔDEF.
उत्तर
It is given that ΔABC ~ ΔDEF.
Therefore, the ration of the areas of these triangles will be equal to the ratio of squares of their corresponding sides.
Also, the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.
Let the altitude of ΔABC be AP, drawn from A to BC to meet BC at P and the altitude of ΔDEF be DQ, drawn from D to meet EF at Q.
`(ar(Δ ABC))/(ar(ΔDEF))=(AP^2)/(DQ^2)`
⇒` 100/49=5^2/(DQ^2)`
⇒ `100/49=25/(DQ^2)`
⇒ `DQ^2=(49xx25)/100`
⇒`DQ=sqrt((49xx25)/100)`
⟹ 𝐷𝑄=3.5 𝑐𝑚
Hence, the altitude of ΔDEF is 3.5 cm
APPEARS IN
संबंधित प्रश्न
In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find 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)`
State, true or false:
Two isosceles-right triangles are similar.
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.
A vertical pole of length 7.5 cm casts a shadow 5 m long on the ground and at the same time a tower casts a shadow 24 m long. Find the height of the tower.
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 the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1cm, PB = 3cm, AQ = 1.5cm, QC = 4.5cm, prove that area of ΔAPQ is 116 of the area of ΔABC.
State the SSS-similarity criterion for similarity of triangles
State the SAS-similarity criterion
In Δ ABC , DE is parallel to BC and `"AD"/"DB" = 2/7` IF AC = 5 .6 , find AE.
Δ ABC ∼ Δ PQR. AD and PS are altitudes from A and P on sides BC and QR respectively. If AD : PS = 4 : 9 , find the ratio of the areas of Δ ABC and Δ PQR.
On a map drawn to a scale of 1 : 25000, a rectangular plot of land, ABCD is measured as AB= 12 cm and BC = 16cm. calculate the diagonal distance of the plot in km and the plot area in km2 .
In the following figure, point D divides AB in the ratio 3 : 5. Find :
BC = 4.8 cm, find the length of DE.
In the given figure, ΔABC ~ ΔADE. If AE : EC = 4 : 7 and DE = 6.6 cm, find BC. If 'x' be the length of the perpendicular from A to DE, find the length of perpendicular from A to BC in terms of 'x'.
In the figure, given below, PQR is a right-angle triangle right angled at Q. XY is parallel to QR, PQ = 6 cm, PY = 4 cm and PX : XQ = 1 : 2. Calculate the lengths of PR and QR.
In the given figure, AB and DE are perpendicular to BC.
- Prove that ΔABC ∼ ΔDEC
- If AB = 6 cm, DE = 4 cm and AC = 15 cm. Calculate CD.
- Find the ratio of the area of a ΔABC : area of ΔDEC.
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD = 4, AE = 8, DB = x - 4 and EC = 3x - 19, find x.
If ΔPQR, AB is drawn parallel to QR. If PQ = 9cm, PR = 6cm and PB = 4.cm, find the length of AP.
In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that TP:TQ = TR:TS
In the given figure, PB is the bisector of ABC and ABC =ACB. Prove that:
a. BC x AP = PC x AB
b. AB:AC = BP: BC
The dimensions of the model of a building are 1.2m x 75cm x 2m. If the scale factor is 1 : 20; find the actual dimensions of the building.
On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The diagonal distance of the plot in km
Construct a triangle similar to a given triangle LMN with its sides equal to `4/5` of the corresponding sides of the triangle LMN (scale factor `4/5 < 1`)
A man whose eye-level is 2 m above the ground wishes to find the height of a tree. He places a mirror horizontally on the ground 20 m from the tree and finds that if he stands at a point C which is 4 m from the mirror B, he can see the reflection of the top of the tree. How height is the tree?
In the given figure YH || TE. Prove that ΔWHY ~ ΔWET and also find HE and TE
Two similar triangles will always have ________ angles
From the figure, prove that ∆SUN ~ ∆RAY
In ∠BAC = 90° and AD ⊥ BC. A then ______.
In the adjoining diagram the length of PR is ______.
