Question

Hypotenuse of a right angled triangle is 2 less than 3 times its shortest side. If the remaining side is 2 more than twice the shortest side, find the area of the triangle.

Answer 1

$let \: \: the \: \: shortest \: \: side \: \: be \: \: x \\ then \: \: hypotenuse = 3x - 2 \\ remaining \: \: side = 2x + 2 \\ for \: \: right \: \: angled \: \: triangle \\ {x}^{2} + {(2x + 2)}^{2} = {(3x - 2)}^{2} \\ {x}^{2} + 4 {x}^{2} + 8x + 4 = 9 {x}^{2} - 12x + 4 \\ 4 {x}^{2} - 20x = 0 \\ 4x(x - 5) = 0 \\ x = 5 \\ \\ area \: \: of \: \: triangle \: = \frac{1}{2} \times x \times (2x + 2) \\ = \frac{1}{2} \times 5 \times 12 = 30$

Answer 2

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