If all three side lengths are INTEGERS and form PYTHAGOREAN TRIPLE then we know decimals are not allowed
if 24 and 51 are both legs then

x = 3177
and squre root of that gives us 56.364.... NOT an integer
So that means one of them is not a leg and since hypotenuse is longer than both legs, 51 must be the hypotenuse so to get the third side
![51^{2} - 24^{2} = x^{2}[tex] [tex] x^{2}](https://tex.z-dn.net/?f=%2051%5E%7B2%7D%20-%20%2024%5E%7B2%7D%20%20%3D%20%20x%5E%7B2%7D%5Btex%5D%20%5Btex%5D%20x%5E%7B2%7D%20)
=2025
x=45, leg B
Answer:
The pairs of integer having two real solution for
are




Step-by-step explanation:
Given

Now we will solve the equation by putting all the 6 pairs so we get the following
for 
for 
for 
for 
for 
for 
The above all are Quadratic equations inn general form 
where we have a,b and c constant values
So for a real Solution we must have

for
we have
which is less than 0 ∴ not a real solution.
for
we have
which is greater than 0 ∴ a real solution.
for
we have
which is greater than 0 ∴ a real solution.
for
we have
which is greater than 0 ∴ a real solution.
for
we have
which is equal to 0 ∴ a real solution.
for
we have
which is less than 0 ∴ not a real solution.
<h3>Given</h3>
1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.
2) Regular pentagon PENTA with side lengths 9 m
<h3>Find</h3>
The area of each figure, rounded to the nearest integer
<h3>Solution</h3>
1) The area of a trapezoid is given by
... A = (1/2)(b1 +b2)h
... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77
The area of BEAR is about 77 cm².
2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...
... A = (1/2)ap
... A = (1/2)(s/(2tan(180°/n)))(ns)
... A = (n/4)s²/tan(180°/n)
We have a polygon with s=9 and n=5, so its area is
... A = (5/4)·9²/tan(36°) ≈ 139.36
The area of PENTA is about 139 m².