The hypotenuse of a right triangle is 10 inches long. One of the legs is 2 inches longer than the other one. If x is the length of the shorter leg, what is the equation

The equation is

X²+2x-48 = 0

Shorter one is 6 inches

Other side= 8 inches

Step-by-step explanation:

The equation for a right angle triangle normally is

A² = B² + C²

Where A = hypotenuse

Then B and C are the order sides of the triangle.

This time

Hypotenuse= 10 inches

The shorter one is X

While the other one is X+2

The equation

10²= x² +(x+2)²

100= x² + x² + 4x +4

100 - 4 = 2x² +4x

96= 2x² +4x

48 = x² +2x

X²+2x-48 = 0

Solving for x

X² +8x-6x-48= 0

X(x+8)-6(x+8)=0

(X-6)(x+8)= 0

X= 6 or x= -8

Definitely x is posiy

So x= 6

Shorter one is 6 inches

Other side= 6+2= 8 inches

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).