Question

THE PERIMETER OF RIGHT ANGLED TRIANGLE IS FIVE TIMES THE LENGTH OF ITS SHORTEST SIDE.THE NUMERICAL VALUE OF THE AREA OF THE TRIANGLE IS 15 TIMES THE NUMERICAL VALUE OF THE LENGTH OF THE SHORTEST SIDE. FIND THE LENGTHS OF THE THREE SIDES OF THE TRIANGLE

Answer 1

Let the sides be x , y, z with z > y > x

As per problem
$x \: + y + z \: = 5x$
$\frac{1}{2} xy = 15x$
$y = 30$
$z = 4x - 30$
By Pythagoras theorem

${z}^{2} = {x}^{2} + {y}^{2}$
${(4x - 30)}^{2} = {x}^{2} + 900$
simplifying

$15 {x}^{2} - 240x = 0$
solving
$x = 0 \: or \: x = 16$
x = 16
y = 30
z = 34