Advertisements
Advertisements
Question
Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are `3/5` of the corresponding sides of the first triangle.
Solution
1. Draw a line AB = 5 cm and draw a ray from A and taking A as centre cut an arc at C of 6 cm and taking B as centre cut an arc of 7 cm at C
2. Draw AX such that ∠BAX is an acute angle.
3. Cut 5 equal arcs AA1, A1A2, A2A3, A3A4, and A4A5.
4. Join A5 to B and draw a line through A3 parallel to A5B which meets AB at B'.
Here, `AB' = 3/5AB`
5. Now draw a line through B' parallel to BC which joins AC at C'.
Here, `B'C' = 3/5BC "and" AC' = 3/5AC`
Thus, AB'C' is the required triangle.
APPEARS IN
RELATED QUESTIONS
In the following figure, in Δ PQR, seg RS is the bisector of ∠PRQ.
PS = 3, SQ = 9, PR = 18. Find QR.
In figure, ∠BAC = 90º and segment AD ⊥ BC. Prove that AD2 = BD × DC.
The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the side BC. Prove that DF × EF = FB × FA
Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that `("AO")/("BO") = ("CO")/("DO")`
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 given figure, ΔOAB ~ ΔOCD. If AB = 8cm, BO = 6.4cm, OC = 3.5cm and CD = 5cm, find (i) OA (ii) DO.
In the given figure, ∠CAB = 90° and AD⊥BC. Show that ΔBDA ~ ΔBAC. If AC = 75cm, AB = 1m and BC = 1.25m, find AD.
ΔABC~ΔDEF and their areas are respectively 64 cm2 and 121cm2. If EF = 15.4cm, find BC.
In ∆ABC and ∆DEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true ?
Δ ABC is similar to Δ PQR. If AB = 6cm, BC = 9cm, PQ = 9cm and PR = 10.5cm, find the lengths of AC and QR.
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
A model of a ship is made with a scale factor of 1 : 500. Find
The length of the ship, if the model length is 60 cm.
A model of a ship is made with a scale factor of 1 : 500. Find
The deck area of the model, if the deck area of the ship is 1500000 m2
A model of a ship is made with a scale factor of 1 : 500. Find
The volume of the ship, if the volume of its model is 200 cm3.
An aeroplane is 30m long and its model is l5 cm long. If the total outer surface area of the model is 150 cm2 , find the cost of painting the outer surface of the aeroplane at Rs. 120 per m2, if 5O m2 is left out for windows.
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 : `(AD)/(AB)`
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
Harmeet is 6 feet tall and casts a shadow of 3 feet long. What is the height of a nearby pole if it casts a shadow of 12 feet long at the same time?
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.
Find the scale factor in each of the following and state the type of size transformation:
Image length = 6cm, Actual length = 4cm.
Find the scale factor in each of the following and state the type of size transformation:
Model area = 75cm2, Actual area = 3cm2
ΔXYZ is enlarged to ΔX'Y'Z'. If XY = 12cm, YZ = 8cm and XZ = 14cm and the smallest side of ΔX'Y'Z' is 12cm, find the scale factor and use it to find the length of the other sides of the image ΔX'Y'Z'.
If figure OPRQ is a square and ∠MLN = 90°. Prove that ∆LOP ~ ∆QMO
A flag pole 15 m high casts a shadow of 3 m at 10 a.m. The shadow cast by a building at the same time is 18.6 m. The height of the building is
ΔABC and ΔBDE are two equilateral triangles such that D is the mid point of BC. Ratio of the areas of triangle ΔABC and ΔBDE is ______.
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.
In the adjoining diagram the length of PR is ______.
