Question

The sides (in cm) of a right angle triangle containing right angle are $5x$ and $(3x-1)$. If the area of the triangle is $60c{m}^2$. Find its perimeter.

• A. $30$ cm
• B. $35$ cm
• C. $40$ cm
• D. $45$ cm

Answer 1

The correct option is C $40$ cm

Area of the right-angled triangle will be
$=\frac{base\times height}{2}$
$=\frac{productofsidescontainingtherightangle}{2}$
$\therefore 60=\frac{5x(3x-1)}{2}$
Hence,
$5x(3x-1)=120$
$3x^2-x-24=0$
$3x^2-9x+8x-24=0$
$3x(x-3)+8(x-3)=0$
$(3x+8)(x-3)=0$
$x=\frac{-8}{3}$ and $x=3$
Now length cannot be negative.
Hence
$x=3$.
Hence the sides are 15cm and 8cm.
Therefore the hypotenuse is
$\sqrt{225+64}$
$=17cm.$
Hence perimeter is
$=40cm$.