Answer:
The perimeter of the triangle is 40.
Step-by-step explanation:
The sum of legs for a right triangle is 12:
[tex] a + b = 21 [/tex]
[tex] a = 21 - b [/tex] (1)
And their product is:
[tex] a*b = 40 [/tex] (2)
By entering eq (1) into (2) we have:
[tex] (21 - b)b = 40 [/tex]
[tex] 21b - b^{2} - 40 = 0 [/tex]
We can find the value of "b" by solving the above quadratic equation.
[tex] b_{1} = 2.1 [/tex]
[tex] b_{2} = 18.9 [/tex]
Since the two values satisfy the equation, we can use either of them to find "a". We will use b₁.
[tex] a = 21 - 2.1 = 18.9 [/tex]
Now, the hypotenuse of the right triangle is given by:
[tex] h = \sqrt{a^{2} + b^{2}} = \sqrt{(18.9)^{2} + (2.1)^{2}} = 19 [/tex]
Hence, the perimeter is:
[tex] P = a + b + h = 18.9 + 2.1 + 19 = 40 [/tex]
Therefore, the perimeter of the triangle is 40.
I hope it helps you!
