Question

tính x,y

Answer 1

Áp dụng HTL

\(\left\{{}\begin{matrix}30^2=x\left(x+32\right)\\y^2=32\left(x+32\right)\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}900=x^2+32x\\y^2=32x+1024\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=18\left(x>0\right)\\y^2=576+1024=1600\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x=18\\y=40\end{matrix}\right.\)

Answer 2

Áp dụng hệ thức lượng trong tam giác vuông có đường cao:

\(30^2=x\left(32+x\right)\)

\(\Rightarrow x^2+32x+256=1156\)

\(\Rightarrow\left(x+16\right)^2=1156\)

\(\Rightarrow x+16=34\Rightarrow x=18\)

\(y^2=32.\left(32+x\right)\)

\(\Rightarrow y^2=32.50\)

\(\Rightarrow y^2=1600\Rightarrow y=40\left(cm\right)\)