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31 January, 10:09

Searches related to The height of a triangle is 4 feet greater than the base. The area of the triangle is 336 square feet. Find the length of the base and the height of the triangle.

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  1. 31 January, 10:27
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    base = 24 ft

    height = 28 ft

    Step-by-step explanation:

    first we have to identify the 2 equations that give us

    h = b+4

    h*b/2 = 336

    Now let's replace the h with (b + 4)

    (b+4) * b/2 = 336

    (b^2+4b) / 2 = 336

    b^2 + 4b = 336*2

    b^2 + 4b = 672

    b^2 + 4b - 672 = 0

    when we have an equation of the form Ax ^ 2 + Bx + C = 0

    we can use bhaskara

    (-B√ (B^2-4AC)) / 2A

    we replace with the values

    (-4√ (4^2-4*1*-672)) / 2*1

    b1 = - 4 + 52 / 2 = 24

    b2 = - 4 - 52 / 2 = - 28

    we can only use positive values

    b = 24

    to know the height we replace b with 24 in the equation of the beginning

    h = b+4

    h = 24+4

    h = 28

    to corroborate we can calculate the area and see if it gives us correct

    h*b/2 = 336

    28*24/2 = 336

    672/2 = 336

    336 = 336

    correct
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