Question

The perimeter of a right angled triangle is 5 times the length of the 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 all the three sides of the triangle.

Answer 1

let the shortest side = a
second shortest side = b
and longest side i.e. hypotenuse = h

then perimeter of the triangle i.e a + b + h = 5a => b +h = 4a => h = 4a - b -----(i)
also
area = 15a
In a rt angled triangle, area will be = 0.5* shortest side * second shortest side (because hypotenuse will be the longest side)
15a = 0.5 * a * b
15a/0.5a = b
30 = b

substitute in (i) we get h = 4a - 30 ------- (ii)

Using Pythagoras Theorem
(4a - 30)^2 = a^2 + 30^2
16a^2 - 240a + 900 = a^2 + 900
16a^2 - a^2 - 240a + 900 - 900 = 0
15a^2 - 240a = 0
a^2 -16a = 0
a(a - 16) = 0
so either a = 0 or a = 16
since length of side of triangle cannot be zero so a = 16
substituting a = 16 in (ii)
h = 4(16) - 30 = 64 - 30 = 34

so we have the three sides as a = 16, b= 30 and h = 34

Answer 2

BRILLIANT answer Harkirat!!!!!! Not only is it right BUT with full explanation that is easy to understand!!!!!! You deserve at least two medals but i can only give one!!


sorry Luis ! your answer is neither right nor does it provide any insight into the solution.

Answer 3

Thanks for appreciating my effort.
if u can't give another medal, u can become my fan .....☺

Answer 4

Sure, why not.