# CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 14 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 24**:

Draw a triangle ABC with side , , . Then construct a triangle whose sides are times the corresponding sides of .

**Answer**:

To construct: To construct a triangle ABC with side , and and then a triangle similar to it whose sides are of the corresponding sides of the first triangle ABC.

Steps of construction:

(a) Draw a triangle ABC with side , and .

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate 4 points and on BX such that .

(d) Join B_{3}C and draw a line through the point , draw a line parallel to intersecting BC at the point C ′ .

(e) Draw a line through parallel to the line to intersect BA at A. ′

Then, A ‘BC’ is the required triangle.

Justification

[By construction]

[AA similarity]

[By Basic Proportionality Theorem]

But [By construction]

Therefore,

[By construction]

[AA similarity]

[From eq. (i) ]

**Question 25**:

Draw a right triangle in which the sides (other than hypotenuse) are of lengths and . Then construct another triangle whose sides are times the corresponding sides of the given triangle

**Answer**:

To construct: To construct a right triangle in which sides (other than hypotenuse) are of lengths and and then a triangle similar to it whose sides are of the corresponding sides of the first triangle ABC.

Steps of construction:

(a) Draw a right triangle in which sides (other than hypotenuse) are of lengths 4 cm and .

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate 5 points and on BX such that .

(d) Join and draw a line through the point , draw a line parallel to intersecting BC at the point C. ′

(e) Draw a line through C ‘parallel to the line CA to intersect BA at A.’

Then, A ‘BC’ is the required triangle.

Justification:

[By construction]

[AA similarity]

[By Basic Proportionality Theorem]

But [By construction]

Therefore,

[By construction]

[AA similarity]

[From eq. (i) ]