Adv
deepaksoni
  • 0
Guru

If the sum of two smaller sides of a right-angled triangle is 17cm and the perimeter is 30cm, then find the area of the triangle.

  • 0

This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
This is an important ques

If the sum of two smaller sides of a right-angled triangle is 17cm and the perimeter is 30cm, then find the area of the triangle.

Question no.19 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

Share

1 Answer

  1. Given,

    The perimeter of the triangle = 30 cm

    Let’s assume the length of one of the two small sides as x cm

    Then, the other side will be (17 – x) cm

    Now, length of hypotenuse = perimeter – sum of other two sides

    = (30 – 17) cm

    = 13 cm

    According to the problem, by Pythagoras theorem we have

    x2 + (17 – x)2 = 132

    x2 + 289 + x2 – 34x = 169

    2x2 – 34x + 289 – 169 = 0

    2x2 – 34x + 120 = 0

    x2 – 17x + 60 = 0 [Dividing by 2]

    By factorization method, we have

    x2 – 12x – 5x + 60 = 0

    x(x – 12) – 5(x – 12) = 0

    (x – 5) (x – 12) = 0

    So,

    (x – 5) = 0 or (x – 12) = 0

    x = 5 or x = 12

    When, x = 5

    First side = 5 cm and second side = (17 – 5) = 12 cm

    And when x = 12

    First side = 12 cm and second side = (17 – 12) = 5 cm

    Thus,

    Area of the triangle = ½ (5 × 12)

    = 60/2

    = 30 cm2

    • 0
Leave an answer

Leave an answer

Browse

Choose from here the video type.

Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions