A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle

Solution:

  • Draw the triangle with the given conditions.

  • Then draw another line that makes an acute angle with the baseline. Divide the line into m + n parts where m and n are the ratios given.

  • Two triangles are called similar if their corresponding angles are equal. They are said to satisfy Angle-Angle-Angle (AAA)

  • The basic proportionality theorem states that “If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionally".

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle 

Steps of constructions:

  1. Draw BC = 4. At B, make an angle ∠CBY = 90° and mark A on BY such that BA = 3 cm. Join A to C. Thus ΔABC is constructed.
  2. Draw the ray BX so that ∠CBX is acute.
  3. Mark 5 (since, 5 > 3 in 5/3) points B₁, B₂, B₃, B₄, B₅ on BX so that BB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B₅
  4. Join B₃ (3rd point on BX as 3 < 5) to C and draw B₅C' parallel to B₃C so that C' lies on the extension of BC.
  5. Draw C'A' parallel to CA to intersect of the extension of BA at A’. Now ΔBA'C' is the required triangle similar to ΔBAC where BA'/BA = BC'/BC = C'A'/CA = 5/3

Proof:

In ΔBB₅C', B₃C || B₃C'

Hence by Basic proportionality theorem,

B₃B₅/BB₃ = CC'/BC = 2/3

CC'/BC + 1 = 2/3 + 1 (Adding 1)

(CC' + BC)/BC = 5/3

BC'/BC = 5/3

Consider ΔBAC and ΔBA'C'

∠ABC = ∠A'BC' = 90°

∠BCA = ∠BC'A' (Corresponding angles as CA || C'A')

∠BAC = ∠BA'C'

By AAA axiom, ΔBAC ~ ΔBA'C'

Therefore, corresponding sides are proportional,

Hence,

BA'/BA = BC'/BC = C'A'/CA = 5/3

☛ Check: NCERT Solutions for Class 10 Maths Chapter 11

Video Solution:

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.

NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.1 Question 7

Summary:

A right triangle ABC in which the sides other than the hypotenuse having lengths 4 cm and 3 cm and another triangle A'BC' whose sides are 5/3 times the corresponding sides of triangle ABC have been constructed.

☛ Related Questions:

Math worksheets and
visual curriculum