3. If sides of the triangle are in the ratio 6:4:5 and its perimeter is 90 on then find the area?​

Question

3. If sides
of the triangle are in the
ratio 6:4:5 and its perimeter is
90 on then find the area?​

in progress 0
Josie 2 months 2021-11-23T04:40:50+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-23T04:42:11+00:00

    AnswEr :

    • Area of the triangle is 135√7 units.

    Given :

    • Sides of a triangle are in ratio 6:4:5.

    To Find :

    • Area of the triangle.

    SoluTion :

    Sides of the triangle are in ratio 6:4:5

    Put x in the ratio

    Then,

    Sides are 6x , 4x , 5x

    Perimeter of a triangle = sum of all sides.

    According to the question

    » 6x + 4x + 5x = 90

    → 15x = 90

    → x = 90/15

    → x = 6

    Put the value of x in the ratio.

    6x = 6 × 6 = 36

    4x = 4 × 6 = 24

    5x = 5 × 6 = 30

    Here,

    a = 36

    b = 24

    c = 30

    We’ve to find semi perimeter of the triangle.

    Formula for finding semi perimeter ( S ) of the triangle is

    » S = a + b + c / 2

    → S = 36 + 24 + 30 / 2

    → S = 90/2

    → S = 45

    Formula for finding area of the triangle is

    » s (s a) (s b) (s c)

    → √45 (45 – 36) (45 – 24) (45 – 30)

    → √45 × 9 × 21 × 15

    1357 units

    Hence, the area of the triangle is 135 units.

    _____________________

    0
    2021-11-23T04:42:34+00:00

    Answer:  357.17 unit sq.

    Step-by-step explanation:Since the ratio is 6:4:5 , let the sides be 6x , 4x and 5x .

    therefore, 6x + 4x + 5x = 90

                   15x = 90

                      x = 90÷15

                      x = 6

    sides are 36 , 24  and 30

    after finding the sides we will find the area by using the heron’s formula

    area = √s(s-a)(s-b)(s-c)

    where s = perimeter/2

    area = √(45)(45-36)(45-24)(45-30)

            = √45×9×21×15

             = 45×3√7

             = 135×2.645

             = 357.17

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