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saul85 [17]
3 years ago
8

The larger leg of a right triangle is 3 cm longer than it's smaller leg.The hypotenuse is 6 cm longer than smaller leg. How many

centimeters long  is the smaller leg
Mathematics
1 answer:
Degger [83]3 years ago
7 0
From the text of the task we have:

smaller leg:   x
longer leg:  x+3
hypotenuse: x + 6

Using the Pythagorean Theorema:

(x+6)^2=x^2+(x+3)^2\\
\\
x^2+12x+36=x^2+x^2+6x+9\\
\\
x^2-6x-27=0\\
\\
\Delta=(-6)^2-4.1.(-27)=36+108=144\\
\\
x=\frac{6 \pm \sqrt{144}}{2}=\frac{6 \pm 12}{2}\\
\\
x_1=-3\\
\\
x_2=9

Obviously -3 is not possible, so, smaller leg is 9 cm
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