IDNLearn.com: Where questions are met with accurate and insightful answers. Ask your questions and get detailed, reliable answers from our community of experienced experts.
Sagot :
[tex]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\\
[/tex]
The length can't be negative, so the answer is 9 cm.
The length can't be negative, so the answer is 9 cm.
Let the smaller leg be x.
Thus, larger leg = 3 +x
Thus, hypotenuse = 6 + x
Applying pythagoras theorum ;
[tex](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[/tex]
Thus, the length of smaller peg is 9 cm.
Thus, larger leg = 3 +x
Thus, hypotenuse = 6 + x
Applying pythagoras theorum ;
[tex](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[/tex]
Thus, the length of smaller peg is 9 cm.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.