The area of a triangle is 36 cm2. The height of the triangle is 6 cm less than the base. What is the height of the triangle? A) 4 cm <

Question

The area of a triangle is 36 cm2. The height of the triangle is 6 cm less than the base. What is the height of the triangle?
A) 4 cm
B) 6 cm
C) 8 cm
D) 12 cm

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Ivy 1 week 2021-10-05T18:32:01+00:00 1 Answer 0

Answers ( )

    0
    2021-10-05T18:33:15+00:00

    Answer:

    Height of triangle = 6 cm

    Step-by-step explanation:

    Let,

    Height of triangle = h

    Base of triangle = b

    Given Data:

    Area of  triangle = A = 36 cm^{2}

    According to given condition:

    h = b – 6

    To find out:  

    Height of triangle = h = ?  

    Formula:  

    Area of  triangle = A = (b × h)/2

    Solution:  

    Area of  triangle = A = (b × h)/2

    36 = (b × h)/2

    36 × 2 = b × (b – 6
    )         ∴h = b – 6

    72 = b^{2}  - 6b

    b^{2}  - 6b - 72 = 0

    b^{2}  - 12b + 6b - 72 = 0

    (b^{2}  - 12b) +( 6b - 72) = 0

    b(b - 12) + 6( b - 12) = 0

    (b - 12)( b + 6) = 0

    b- 12 = 0       or    b + 6 = 0

    b = 12           or    b = -6

    As base value is always positive, so

    Base of triangle = b = 12 cm

    h = b – 6

    h = 12 – 6

    Height of triangle = 6 cm

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45:7+7-4:2-5:5*4+35:2 =? ( )