Download App

Constructions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsConstructions5 Marks
Question
Construct a $\triangle\text{ABC}$ in which AB = 5cm, $\angle\text{B} = 60^\circ,$ altitude CD = 3cm. Construct a $\triangle\text{AQR}$ similar to $\triangle\text{ABC}$ such that side of $\triangle\text{AQR}$ is 1.5 times that of the corresponding sides of $\triangle\text{ABC}.$
✓

Answer

Steps of construction:
i. Draw a line segment $A B=5 cm$.
ii. At $A$, draw a perpendicular and cut off $A E=3 cm$.
iii. From E, draw EF || AB.
iv. From $B$, draw a ray making an angle of 60 meeting $E F$ at $C$.
v. Join CA. Then $A B C$ is the triangle.
vi. From $A$, draw a ray $A X$ making an acute angle with $A B$ and cut off 3 equal parts making $A A_1=A_1 A_2=A_2 A_3$.
vii. Join $A_2$ and $B$.
iiii. From $A$, draw $A^{\prime} B^{\prime}$ parallel to $A_2 B$ and $B^{\prime} C^{\prime}$ parallel to $B C$.
Then $\triangle\text{C}'\text{AB}'$ is the required triangle.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Constructions→Constructions — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

From a solid cylinder whose height is 15 cm and diameter 16 cm , a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. [Take $\pi=3.14$ ]
→
Find the values of a and b for which the following system of equations has infinitely many solutions:
$3x + 4y = 12$
$(a + b)x + 2(a - b)y = 5a - 1$
→
The ratio of the sums of first $m$ and first $n$ terms of an A. P. is $m^2: n^2$.
Show that the ratio of its $m^{th}$ and $n^{th}$ terms is $(2 m-1):(2 n-1)$.
→
If $BD$ and $QM$ are medians of triangles $\text{ABC}$ and $\text{PQR},$ respectively, where $\triangle ABC \sim \triangle PQR$ prove that $\frac{A B}{P Q}=\frac{B D}{Q M}$.
→
Find the median wages for the following frequencies distribution:
Wages per day (in Rs).
61-70
71-80
81-90
91-100
101-110
111-120
No. of women workers.
5
15
20
30
20
8
→
If Nidhi were $7$ years younger than what she actually is, then the square of her age $($in years$)$ would be $1$ more than $5$ times her actual age. What is her present age ?
→
Two identical cubes each of volume $64cm^3 $are joined together end to end. What is the surface area of the resulting cuboid?
→
Prove the following trigonometric identities.
$\frac{\tan^3\theta}{1+\tan^2\theta}+\frac{\cot^3\theta}{1+\cot^2\theta}=\sec\theta\text{cosec}\theta-2\sin\theta\cos\theta$
→
If the mean of the following frequency distribution is 54, find the value of p.
Class
0-20
20-40
40-60
60-80
80-100
Frequency
7
p
10
9
13
→
Solve the following quadratic equation by factorization:
$3\Big(\frac{3\text{x}-1}{2\text{x}+3}\Big)-2\Big(\frac{2\text{x}+3}{3\text{x}-1}\Big)=5,$ $\text{x}\neq\frac{1}{3},-\frac{3}{2}$
→