Question

In a right angled triangle one of the sides forming the right angle is 4 cm more than twice the
length of the other side. If the area of the triangle is 120cm², find perimeter of the triangle.​

Answer 1

$let \: one \: side \: be \: x \\ second \: side = 4 + 2x$

$area = \frac{1}{2} \times x \times 4 + 2x \\ 120 \times 2 = 4 x+ 2x \\ 240 = 6x \\ x = \frac{240}{6} = 40cm$

$one \: side = 40cm \\ second \: side = 4 + 2 \times 40 \\ = 4 + 80 = 84cm$

$third \: side = \sqrt{ {84}^{2} - {40}^{2} } \\ = \sqrt{7056 - 1600} \\ = \sqrt{5456} = 73.86$