Advertisements
Advertisements
Questions
In figure, ∆ACB ~ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm, AP = 2.8 cm, find CA and AQ.
In the following figure, ΔACB ~ ΔAPQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.
Solution
We have, ∆ACB ~ ∆APQ
`\Rightarrow \frac{AC}{AP}=\frac{CB}{PQ}=\frac{AB}{AQ} `
`\Rightarrow \frac{AC}{AP}=\frac{CB}{PQ}\text{ and }\frac{CB}{PQ}=\frac{AB}{AQ}`
`\Rightarrow \frac{AC}{2.8}=\frac{8}{4}\text{ and }\frac{8}{4}=\frac{6.5}{AQ} `
`\Rightarrow \frac{AC}{2.8}=2\text{ and }\frac{6.5}{AQ}=2`
AC = (2 × 2.8) cm = 5.6 cm and `AQ=\frac{6.5}{2}cm=3.25cm`
APPEARS IN
RELATED QUESTIONS
Examine each pair of triangles in Figure, and state which pair of triangles are similar. Also, state the similarity criterion used by you for answering the question and write the similarity relation in symbolic form
figure (i)
figure 2
figure 3
figure 4
figure 5
figure 6
figure 7
Prove that the line segments joining the mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles
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)`
Given: FB = FD, AE ⊥ FD and FC ⊥ AD.
Prove that: `(FB)/(AD) = (BC)/(ED)`.
In the figure, given below, the medians BD and CE of a triangle ABC meet at G. Prove that:
- ΔEGD ~ ΔCGB and
- BG = 2GD from (i) above.
The given figure shows a trapezium in which AB is parallel to DC and diagonals AC and BD intersect at point P. If AP : CP = 3 : 5,
Find:
- ∆APB : ∆CPB
- ∆DPC : ∆APB
- ∆ADP : ∆APB
- ∆APB : ∆ADB
The given figure shows a triangle PQR in which XY is parallel to QR. If PX : XQ = 1 : 3 and QR = 9 cm, find the length of XY.
Further, if the area of ΔPXY = x cm2; find, in terms of x the area of :
- triangle PQR.
- trapezium XQRY.
ABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the midpoints of AB, AC, CD and BD respectively, show that PQRS is a rhombus.
In ΔABC, D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.
In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.
O is any point in the interior of ΔABC. Bisectors of ∠AOB, ∠BOC and ∠AOC intersect side AB, side BC, side AC in
F, D and E respectively.
Prove that
BF × AE × CD = AF × CE × BD
Δ ABC - Δ XYZ. If area of Δ ABC is 9cm2 and area of Δ XYZ is 16cm2 and if BC= 2.1cm, find the length of YZ.
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.
The scale of a map is 1 : 200000. A plot of land of area 20km2 is to be represented on the map. Find:
The area in km2 that can be represented by 1 cm2
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 given figure, PQ || AB; CQ = 4.8 cm QB = 3.6 cm and AB = 6.3 cm. Find : PQ
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC.
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD = 8cm, AB = 12cm and AE = 12cm, find CE.
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: Area of quadrilateral PBCQ: area of ΔABC.
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, ∠ABC = 90°. Calculate:
(i) The actual length of AB in km.
(ii) The area of Plot in sq. km.
Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y
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`)
If BD ⊥ AC and CE ⊥ AB, prove that `"CA"/"AB" = "CE"/"DB"`
Two similar triangles will always have ________ angles
ΔPQR ~ ΔSUV. Write pairs of congruent angles
If ∆ABC ~ ∆QRP, `(ar(ABC))/(ar(PQR)) = 9/4`, AB = 18 cm and BC = 15 cm, then PR is equal to ______.
In ΔPQR, S and T are points on PQ and PR respectively. `(PS)/(SQ) = (PT)/(TR)` and ∠PST = ∠PRQ. Prove that PQR is an isosceles triangle.
