Question

2. La hipotenusa de un triangulo rectángulo mide 50cm y uno de sus catetos mide 35cm. Cuánto mide el otro cateto.? (2 puntos) 36 25 32 38 ​

Answer 1

【Rpta.】El otro cateto del triángulo rectángulo mide aproximadamente 35.71 cm.

                              $\green{{\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedimiento}}{\hspace{50pt}\above 1.2pt}}$

Para determinar cuánto mide el otro cateto utilizaremos el Teorema de Pitágoras

                                             $\overset{\displaystyle \overset{\overset{\displaystyle \boldsymbol{\mathsf{a}}}{\dfrac{}{}}}{\frac{}{}}\hspace{-35pt}\overset{\displaystyle \overset{\displaystyle\overset{\hspace{1pt}\big|\! \displaystyle \diagdown}{\hspace{25pt}\big|\hspace{11pt}\diagdown \:\:\:\boldsymbol{\mathsf{c}}}}{\hspace{25pt}\big|\hspace{23pt}\diagdown}}{\hspace{32pt}\:\ \big|_{\hspace{-3pt}\blacksquare_{{\hspace{32pt}\above 0.2pt}}}\hspace{-10pt}\:\:\:\diagdown}}{\boldsymbol{\mathsf{b}}}\hspace{30pt}$

                                       ${\above 3pt{\boxed{\overset{\boldsymbol{\mathsf{\underline{TEOREMA\: DE\: PIT\acute{A}GORAS}}}}{\overset{}{\mathsf{c^2 = a^2 + b^2}}}}\above 3pt }}$

Extraemos los datos del enunciado

                    $\begin{array}{ccccccccccccc}\mathsf{\triangleright\:\:\:c=50\:cm}&&&&&&&&&&& \mathsf{\triangleright\:\:\:a=35\:cm}\end{array}$

Reemplazamos

                                       $\begin{array}{c}\mathsf{c^2=a^2+b^2}\\\\\mathsf{(50\:cm)^2=(35\:cm)^2+b^2}\\\\\mathsf{2500\:cm^2=1225\:cm^2+b^2}\\\\\mathsf{b^2=2500\:cm^2-1225\:cm^2}\\\\\mathsf{b^2=1275\:cm^2}\\\\\mathsf{b=\sqrt{1275\:cm^2}}\\\\\mathsf{\boxed{\boxed{\boldsymbol{\mathsf{b\approx 35.71\:cm}}}}}\end{array}$

                                         $\boxed{\sf{{R}}\quad\raisebox{10pt}{ \sf{\red{O}} }\!\!\!\!\raisebox{-10pt}{ \sf{\red{O}} }\quad\raisebox{15pt}{ \sf{{G}} }\!\!\!\!\raisebox{-15pt}{ \sf{{G}} }\quad\raisebox{15pt}{ \sf{\red{H}} }\!\!\!\!\raisebox{-15pt}{ \sf{\red{H}} }\quad\raisebox{10pt}{ \sf{{E}} }\!\!\!\!\raisebox{-10pt}{ \sf{{E}} }\quad\sf{\red{R}}}\hspace{-64.5pt}\rule{10pt}{.2ex}\:\rule{3pt}{1ex}\rule{3pt}{1.5ex}\rule{3pt}{2ex}\rule{3pt}{1.5ex}\rule{3pt}{1ex}\:\rule{10pt}{.2ex}$

Answer 2

Respuesta:

utilizamos formula de pitagoras

a^{2} = b^{2} + c^{2}a

2

=b

2

+c

2

reemplazamos :

\begin{gathered}50^{2} = 35^{2} + c^{2} \\\\2500 = 1225 + c^{2}\\\\c^{2} = 2500 - 1225\\\\c^{2} = 1275\\\\c = \sqrt{1275} \\\\c= 5\sqrt{51}\end{gathered}

50

2

=35

2

+c

2

2500=1225+c

2

c

2

=2500−1225

c

2

=1275

c=

1275

c=5

51

explicación paso a paso:espero y te ayude