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earnstyle [38]
2 years ago
9

The larger leg of a right triangle is 3cm longer than its smaller leg. The hypotenuse is 6cm longer than the smaller leg. how ma

ny centimeters long is the smaller leg  
please explain how you got it 

Mathematics
2 answers:
Viktor [21]2 years ago
7 0
Let the smaller leg be x.

Thus, larger leg = 3 +x
Thus, hypotenuse = 6 + x

Applying pythagoras theorum ;

(6+x)^2 = x^2 + (3+x)^2 \\ \\ or, 6^2 + 12x + x^2 = 3^2 + 6x + x^2 \\ \\ i.e., 36 + 12x = 9 + 6x \\ \\ =>6x = 45 \\ \\ => x = 9

Thus, the length of smaller peg is 9 cm.
Natalka [10]2 years ago
5 0
b=a+3\\
c=a+6\\
a^2+b^2=c^2\\\\
a^2+(a+3)^2=(a+6)^2\\
a^2+a^2+6a+9=a^2+12a+36\\
a^2-6a-27=0\\
a^2-9a+3a-27=0\\
a(a-9)+3(a-9)=0\\
(a+3)(a-9)=0\\
a=-3 \vee a=9\\


The length can't be negative, so the answer is 9 cm.

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