shoter leg = x
longer leg = 3x+3
to solve for hypotenuse you use
a^2 + b^2 = c^2, so
(x)^2 + (3x+3)^2 = (4x-3)^2
(x)(x) + (3x+3)(3x+3) = (4x-3)(4x-3)
(x^2) + (9x^2+18x+9) = (16x^2-24x+9)
then combine like terms
10x^2 + 18x + 9 = 16x^2 - 24x + 9
then i subtracted 10x^2 from both sides
18x + 9 = 6x^2 - 24x +9
next, i subtracted 18x from both sides:
9 = 6x^2 - 42x + 9
and then subtracted 9 from both sides
0 = 6x^2 - 42x
then pull out a 6x on the right side of the equation
0 = 6x(x-7)
so x= 0 and 7
so the shorter leg is :
0 units or 7 units
the longer leg is :
3 units or 24 units
and the hypotenuse is :
-3 units or 25
and since you cant have a hypotenuse with a negative value
i think the three lengths of your triangle are
7, 24, and 25
Thanks for the help. :)
Answer this Question
math - The hypotenuse of a right triangle is 1 cm more than twice the shorter ...
math - did i do this right? The hypotenuse of a 30 ¨C 60-90 right triangle ...
Algebra - the length of the longer leg of a right triangle is 13 ft more than 3 ...
Math - A toy manufacturer needs a piece of plastic in the shape of a right ...
math - The longer leg of a right triangle is 3 more than the shorter leg. The ...
Math - The shorter leg of a right triangle is 14 feet shorter than the longer ...
Algebra - A lot is in the shape of a right triangle. The shorter leg measures 90...
Algebra - The hypotenuse of a right triangle is 5cm long. One leg is 3cm longer ...
Algebra - the longer legs of a right triangle is 20 cm more than twice the ...
math - The shorter leg of a 30°–60°–90° triangle is 10. What are the lengths of ...