Download App

Constructions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsConstructions5 Marks
Question
Construct a $\triangle\text{ABC},$ in which BC = 5cm, $\angle\text{C}=60^\circ$ and altitude from A is equal to 3cm. Construct a $\triangle\text{ADE}$ similar to $\triangle\text{ABC},$ such that each side of $\triangle\text{ADE}$ is $\frac32$ times the corresponding side of $\triangle\text{ABC}$ Write the steps of construction.
✓

Answer


Step of constuction:
  1. Draw a line segment BC = 5cm
  2. Construct $\angle\text{BCP}=60^\circ$
  3. Draw a line GH || BC at a distance of 3cm, intersecting CP at A.
  4. Join AB and draw altitude $\text{AM}\perp\text{BC}.$ Thus, $\triangle\text{ABC}$ is obtained.
  5. Extend AB to D such that $\text{AD}=\frac32\text{AB}.$
  6. Draw DE || BC, cutting AC produced at E.
Then, $\triangle\text{ADE}$ is the required triangle similar to $\triangle\text{ABC}$ such that each side of $\triangle\text{ADE}$ is $\frac32\text{times}$ the corresponding side of $\triangle\text{ABC}$

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

Two triangles ABC and PQR are such that AB = 3cm, AC = 6cm, $\angle\text{A}=70^\circ,\text{PR}=9\text{cm},\angle\text{P}=70^\circ$ and $\text{PQ}=4.5\text{cm}.$ show that $\triangle\text{ABC}\sim\triangle\text{PQR}$ and state the similarity criterion.
→
$\text{l}\parallel\text{m}$ and line segments AB, CD and EF are concurrent at point P. Proved that $\frac{\text{AE}}{\text{BF}}=\frac{\text{AC}}{\text{BD}}=\frac{\text{CE}}{\text{FD}}.$
→
A is a point at a distance 13cm from the centre O of a circle of radius 5cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the $\triangle\text{ABC}.$
→
Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.
→
The perimeter of a right triangle is 40cm and its hypotenuse measures 17cm. Find the area of the triangle.
→
Find the area of a quadrant of a circle whose circumference is 88cm. $[\text{Take }\pi\ =3.14]$
→
In the given figure, common tangents $A B$ and $C D$ to the two circles with centres $O_1$ and $O_2$ intersect at $E$. Prove that $A B=C D$.
→
A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.
→
Construct a $\triangle\text{ABC},$ with BC = 7cm, $\angle\text{B}=60^\circ$ and AB = 6cm. Construct another triangle whose sides are $\frac34\text{times}$ the corresponding sides of $\triangle\text{ABC}.$
→
The sum of two numbers is 137 and their difference is 43. Find the numbers.
→