Question
Construct a triangle using the following data: $XY + YZ = 5.6 \ cm, XZ = 4.5 \ cm$ and $\angle X = 45^\circ $
✓
Answer
$XY + YZ = 5.6 \ cm, XZ = 4.5 \ cm$ and $\angle X = 45^\circ $
Steps of construction:
$1$. Draw a line segment $XZ = 4.5 \ cm$
$2$. With $X$ as centre, construct $\angle SXZ = 45^\circ $
$3$. Cut $XT = 5.6 \ cm$ on $XS.$
$4$. Join $TZ.$
$5$. Draw perpendicular bisector of $TZ$ which cuts $XT$ at $Y$.
$6.$ Join $YZ.$
Thus $\text{XYZ}$ is the required triangle.
Steps of construction:
$1$. Draw a line segment $XZ = 4.5 \ cm$
$2$. With $X$ as centre, construct $\angle SXZ = 45^\circ $
$3$. Cut $XT = 5.6 \ cm$ on $XS.$
$4$. Join $TZ.$
$5$. Draw perpendicular bisector of $TZ$ which cuts $XT$ at $Y$.
$6.$ Join $YZ.$
Thus $\text{XYZ}$ 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.
Explore more
Similar questions
Make $f$ the subject of the formula $D=\sqrt{\left(\frac{f+p}{f-p}\right)}$. Find $f_r$ when $D=13$ and $P=21$.
→If the equal sides of an isosceles triangle are produced, prove that the exterior angles so formed are obtuse and equal.
In the given figure, $AD$ is perpendicular to $BC.$ Find $: 5\cos x - 12\sin y +\tan x$
→Draw a graph of the equation $2x - 3y = 15$. From the graph find the value of:$(i) x$, when $y = 3;(ii) y$, when $x = 0$
→If $\tan x^{\circ}=\frac{5}{12} \cdot \tan y^{\circ}=\frac{3}{4}$ and $A B=48\ m ;$ find the length $C D$.
→A two$-$digit number is such that the ten's digit exceeds thrice the unit's digit by $3$ and the number obtained by interchanging the digits is $2$ more than twice the sum of the digits. Find the number.
→Find the interior angles of the following triangles:
In a quadrilateral $\text{ABCD}, AB = AD$ and $CB = CD$.Prove that :$(i) AC$ bisects $\angle BAD.(ii) AC$ is the perpendicular bisector of $BD.$
→One day three friends Amit (A), Binay (B) and Chanchal (C) were playing hide and seek game in the park of their society. Amit and Binay hide in the shrubs and Chanchal has to find both of them. If the position of three friends are at A, B and C respectively, as shown in the figure and forms a right angled triangle ABC such that AB = 6m, $B C=2 \sqrt{3} m$ and $\angle B =90$.
Based on the above information, answer the following questions :
Q.1. The length of AC is :
(a) 4 m (b) $8 \sqrt{3} m$ (c) $5 \sqrt{3} m$ (d) $4 \sqrt{3} m$
Q.2. The measure of $\angle A$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.3. The measure of $\angle C$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.4. $\cos 2 A$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\frac{\sqrt{3}}{2}$ (d) $\sqrt{3}$
Q.5. $2 \sin \left(\frac{ C }{2}\right)$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\sqrt{3}$ (d) $\frac{\sqrt{3}}{2}$
→Based on the above information, answer the following questions :
Q.1. The length of AC is :
(a) 4 m (b) $8 \sqrt{3} m$ (c) $5 \sqrt{3} m$ (d) $4 \sqrt{3} m$
Q.2. The measure of $\angle A$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.3. The measure of $\angle C$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.4. $\cos 2 A$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\frac{\sqrt{3}}{2}$ (d) $\sqrt{3}$
Q.5. $2 \sin \left(\frac{ C }{2}\right)$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\sqrt{3}$ (d) $\frac{\sqrt{3}}{2}$
Find the value of $' y\ '$ if $\sqrt{3}=1.723$.Given your answer correct to $2$ decimal places.
→