The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete

Discussion in 'Calculator Requests' started by math_celebrity, Apr 26, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000.

    • h = b + 70
    • A = 1/2bh = 3000
    Substitute the height equation into the area equation
    1/2b(b + 70) = 3000

    Multiply each side by 2
    b^2 + 70b = 6000

    Subtract 6000 from each side:
    b^2 + 70b - 6000 = 0

    Using our quadratic calculator, we get:
    b = 50 and b = -120

    Since the base cannot be negative, we use b = 50.

    If b = 50, then h = 50 + 70 = 120

    The perimeter is b + h + hypotenuse

    Using the right-triangle calculator, we get hypotenuse = 86.02

    Adding up all 3 for the perimeter: 50 + 70 + 86.02 = 206.02

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