Answer:
[tex]w=8cm\\h=18.75cm[/tex]
Step-by-step explanation:
Let:
[tex]w=Width\\h=Initial\hspace{3}height\\h_m=Modified\hspace{3}height\\\\Where:\\\\h_m=h-3[/tex]
The area of the cardboard can be calculated using the formula to find the area of a rectangle:
[tex]A=w*h[/tex]
The area of the new cardboard would be:
[tex]A=w*h_m\\\\Where:\\\\w=8\\h_m=h-3\\A=126[/tex]
So:
[tex]126=8*(h-3)\\\\126=8h-24[/tex]
Solving for h:
[tex]126+24=8h\\\\150=8h\\\\h=\frac{150}{8} =\frac{75}{4} =18.75cm[/tex]
Therefore, the dimensions of the initial cardboard are:
[tex]w=8cm\\h=18.75cm[/tex]
Translation:
Sea:
[tex]w=Ancho\\h=Altura\hspace{3}inicial\\h_m=Altura\hspace{3}modificada\\\\Donde:\\\\h_m=h-3[/tex]
El área de la cartulina se puede calcular usando la fórmula para encontrar el área de un rectángulo:
[tex]A=w*h[/tex]
El área de la nueva cartulina sería:
[tex]A=w*h_m\\\\Donde:\\\\w=8\\h_m=h-3\\A=126[/tex]
Entonces:
[tex]126=8*(h-3)\\\\126=8h-24[/tex]
Resolviendo para h:
[tex]126+24=8h\\\\150=8h\\\\h=\frac{150}{8} =\frac{75}{4} =18.75cm[/tex]
Por lo tanto, las dimensiones de la cartulina inicial son:
[tex]w=8cm\\h=18.75cm[/tex]
