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Solution - Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle whose sides are `3/4`times the corresponding sides of the isosceles triangle. - CBSE Class 10 - Mathematics

ConceptConstructions Examples and Solutions

Question

Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle whose sides are `3/4`times the corresponding sides of the isosceles triangle.

Solution

Let ABC be an isosceles triangle with AB = AC, base BC = 6 cm and altitude AD = 4 cm.

A ΔA'BC', whose sides are 34 times the sides of ΔABC, can be drawn using the following steps:

1. Draw a line segment BC of 6 cm. Draw arcs of the same radius on both sides of the line segment while taking points B and C as its centre. Let these arcs intersect each other at O and O'. Join OO'. Let OO' intersect BC at D

2. Taking D as centre, draw an arc of 4 cm radius which cuts the line segment OO' at point A. An isosceles ΔABC is formed, having altitude (AD) as 4 cm and base (BC) as 6 cm.

3. Draw a ray BX making an acute angle with line segment BC on the opposite side of vertex A.

4. Locate 4 points (as 4 is greater between 3 and 4) B1, B2, B3 and B4 on BX such that BB1 = B1B2 = B2B3 = B3B4.

5. Join CB4 and draw a line through B3 parallel to CB4 to intersect line segment BC at point C'.

6. Draw a line through C' parallel to AC intersecting line segment AB at A'.

Thus, ΔA'BC' is the required triangle

Is there an error in this question or solution?

Reference Material

Solution for question: Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle whose sides are `3/4`times the corresponding sides of the isosceles triangle. concept: null - Constructions Examples and Solutions. For the course CBSE
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