Question

The base area of a triangle is greater than twice the height 3cm. If the area of the triangle is 44cm² find the base and height of the triangle.

Answer 1

$\huge \underline \bold \green{QUESTION}:$

The base of a triangle is greater than twice the height by 3cm. If the area of the triangle is 44cm² find the base and height of the triangle.

( corrected )

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$\huge \underline \bold \red{SOLUTION}:$

$let \: the \: base \: be \: x \: \\ then \: the \: height \: will \: be \: 2x + 3 \\ we \: know \: that \: the \: \\ area \: of \: triangle \: = \frac{1}{2} \times base \times height \: \\ given \: that \: area \: = 44 {cm}^{2} \\ we \: know \: base \: and \: the \: height \: so \: we \: use \: \\ = > \frac{1}{2} \times x \times (2x + 3) = 44 \\ = > x(2x + 3) = 88 \\ = > 2 {x}^{2} + 3x - 88 = 0 \\ = > {x}^{2} + 11x - 8x - 88 = 0 \\ = > x(x + 11) - 8(x + 11) = 0 \\ = > (x - 8)(x + 11) = 0 \\ = > x = 8 \: or \: ( - 11) \: \\ distance \: is \: always \: positive \: so \: \\ \: \boxed{ x = 8} \: \\ \: \: \: \: \: is \: the \: answer$

$</p><p> \huge\underline\bold \red{final \: answer}$

$the \: base \: of \: the \: triangle \: \\ = > base \: = x = 8 \\ = > height \: = \: 2x + 3 = 2(8) + 3 = 19 \\ = > therefore \\ \: \boxed {base = 8} \\ \boxed{height = 19}$

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