Question

The larger leg of a right triangle is 3 cm longer than its smaller leg. The hypotenuse is 6 cm longer than the smaller leg. How many centimeters long is the smaller leg?

Answer 1

To find the length of the smaller leg of the right triangle, we can use the Pythagorean theorem and solve the equation.

Step-by-step explanation:

Let x be the length of the smaller leg of the right triangle. The larger leg is 3 cm longer, so its length is x + 3. The hypotenuse is 6 cm longer, so its length is x + 6.

According to the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we have the equation: x^2 + (x + 3)^2 = (x + 6)^2.

Solving this equation will give us the value of x, which is the length of the smaller leg.

Answer 2

I will choose the symbol * to expess square

(x)*+(X+3)*=(x+6)*

x*+(X*+6x+9)=x*+12x+36)

2x*+6x+9=x*+12x+36

2x*-x*+6x-12x+9-36=0

x*-6x-27=0

factor this:

(x+3) (x-9)=0

(x+3)=0 x=-3 NO

(x-9) x=9 YES

SMALL SIDE 9

MEDIAN 9+3=12

HYPOTENUSE 9+6=15

9*+12*=15*

81+144=225

225=225