The lengths of the leg : <u>12 and 5</u>
<h3>Further explanation
</h3>
Quadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
![\large {\boxed {\bold {f (x) = ax ^ 2 + bx + c}}}](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7B%5Cbold%20%7Bf%20%28x%29%20%3D%20ax%20%5E%202%20%2B%20bx%20%2B%20c%7D%7D%7D)
where a, b, and c are real numbers and a ≠ 0.
There are 3 ways to solve quadratic equations
a. factoring b. perfect squared c. quadratic formula
We use the factoring method
Quadratic equation x² + bx + c = 0 is equivalent to quadratic equation
![{\displaystyle {x ^ 2 + (p + q) \times \: pq}}](https://tex.z-dn.net/?f=%7B%5Cdisplaystyle%20%7Bx%20%5E%202%20%2B%20%28p%20%2B%20q%29%20%5Ctimes%20%5C%3A%20pq%7D%7D)
where p + q = b and px q = c
for a = 1, the result of factoring is (x + p) (x + q)
If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle
There is a hypotenuse in this triangle which is the sum of the two sides
<h3>c² = a² + b²</h3>
where c = hypotenuse
This formula is known as the Pythagorean theorem which states that:
the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides.
- The hypotenuse of a right triangle is 13 inches
then c = 13
- If the long leg is 7 inches longer than the short leg
then a = b + 7
Then the phytagorean equation becomes:
(b + 7)² + b² = 13²
49+14b+b²+b²=169
49+14b+2b²=169
2b²+14b-120=0
b²+7b-60=0
factoring
(b-5)(b+12)=0
b=5 or b=-12
we use positive number ⇒5
So :
the long leg = b+7=5+7=12
the short leg = b = 5
<h3>
Learn more
</h3>
the triangle angle
brainly.com/question/1611320
Prove the converse of the Pythagorean Theorem
brainly.com/question/1597216
Use Pythagoras' theorem
brainly.com/question/10488367
Keywords : Pythagorean Theorem
, hypotenuse, the long leg