Perimeter of a right triangle is 12cm and its hypotenuse is of length 5cm. Find the other two sides and calculate it's area?

##= color(purple)(6cm^2##

A very frequently observed Pythagorean triplet is : ##color(red)(3,4,5## This triplet perfectly fits the conditions provided in the question as :

• Perimeter : ##3+4+5 = 12cm##
• and, ##5cm## perfectly fits as the hypotenuse(as it is the largest of all sides)

So it is a right angled triangle of base and height: ##3,4##

Area of a right angled triangle : ##color(purple)(area = 1/2##(base.height) ##= 1/2(3.4)## ##= color(purple)(6cm^2##