CAT Question  >  The lengths of three sides of a triangle are ... Save

Related Test

The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles? 
    Correct answer is '2'. Can you explain this answer?

    Answers

    Solution: An isosceles triangle has two sides equal. We have three cases:
    Case (i): x + 7 = 9 - 2x
    3x = 2. x = 2/3, which is not an integer.
    Case (ii): x + 7 =  3x - 1
    2x = 8,  x = 4
    The sides are 11,11 and 1
    Case (iii): 9 - 2x = 3x - 1, 5x = 10, x = 2 The sides are 5, 5 and 9
    The triangle is isosceles for two values of x. 
    Answer: 2

    View courses related to this question
    Explore CAT courses
    Explore CAT courses
    View courses related to this question
    1 Crore+ students have signed up on EduRev. Have you?

    Similar CAT Doubts

    • Directions: In a square of side 10 m, an isosceles triangle is placed on on... more

    • 1 Answer

    Question Description
    The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer?.
    Solutions for The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
    Here you can find the meaning of The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer?, a detailed solution for The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer? has been provided alongside types of The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?Correct answer is '2'. Can you explain this answer? tests, examples and also practice CAT tests.
    Solution: An isosceles triangle has two sides equal. We have three cases:Case (i): x + 7 = 9 - 2x3x = 2. x = 2/3, which is not an integer.Case (ii): x + 7 = 3x -12x = 8, x = 4The sides are 11,11 and 1Case (iii): 9 - 2x = 3x - 1, 5x = 10, x = 2 The sides are 5, 5 and 9The triangle is isosceles for two values of x.Answer: 2