A right triangle has one leg that is 5 cm longer than the other leg and the hypotenuse is 25 cm long. How do you find the length of each leg?
No such triangle exists.
If we denote the shorter leg as
Since neither of these are possible for any real triangle,
no triangle exists that meets the given conditions.
15cm and 20cm.
Since it is a right triangle use
#color(blue) " Pythagoras's Theorem"#
which states 'in a right triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides'
This can be written as an equation. If c is the hypotenuse and a and b are the other 2 sides ( the legs ) then
# c^2 = a^2 + b^2#
Here , let one of the legs be x , so the other is x + 5
#25^2 = x^2 + (x+5)^2 " using theorem "#
now distribute brackets and collect like terms. Also going to reverse the equation so x terms are on the left side.
#x^2 + x^2 + 10x +25 = 625#
#2x^2 + 10x +25 = 625#
this is a quadratic equation , hence equate to zero to solve.
#2x^2 + 10x - 600 = 0 #
common factor of 2 :
# 2(x^2 + 5x -300) = 0 #
Require factors of -300 which sum to 5 (coefficient of x term). These are +20 and - 15 . If unsure use quadratic formula to obtain them.
#rArr 2(x+20)(x-15) = 0#
the solution is x = - 20 or x = 15 : x > 0 thus x = 15
The 2 legs are x and x+5 hence 15 and 20.