Question

In a right angled triangle, perimeter of triangle is 12cm and its hypotenuse is of length 5 cm. Find the other two sides with sensible steps.
PLEASE ANSWER fast with steps

Answer 1

let the two legs of the triangle be x and y.
Then x+y+5=12 and x^2+y^2=5^2
y=7−x
x^2+(7−x)2=25
x^2+49−14x+x^2=25
2x2−14x+24=0
2(x^2−7x+12)=0
2(x−3)(x−4)=0
x=3and4
The two legs measure 3 and 4 cm.
The triangle has sides of 3,4and5 centimetres. 

Answer 2

Let the other sides be x and y.

So, x + y + 5 = 12

x + y = 7

y = 7 - x ..............Equation (1)

Using Pythagoras Theorem,

5² = x² + y²

Substituting value of y from equation (1)

25 = x² + (7 - x)²

25 = 2x² - 14x + 49

2x² -14x + 24 = 0

x² - 7x + 12 = 0

x² - 4x - 3x + 12 = 0

x(x - 4) - 3(x -4) = 0

(x - 3)(x - 4) = 0

So, x = 3,4

If x = 3 then y = 4

and if x = 4 then y = 3.

Thank you.