Respuesta :
Answer:
15 cm by 12 cm.
Step-by-step explanation:
Given:
Amanda uses a rectangular canvas for a panting.
The length is [tex]6x-3[/tex] centimeters.
The width is [tex]2x+6[/tex] centimeters, and is 4/5 of the length .
Question asked:
.What are the dimensions of the canvas ?
Solution:
As given that the width is [tex]\frac{4}{5}[/tex] of the length.
[tex]2x+6=\frac{4}{5} (6x-3)\\ \\ 2x+6=\frac{4}{5}\times6x-\frac{4}{5}\times3\\ \\ 2x+6=\frac{24x}{5} -\frac{12}{5} \\ \\[/tex]
Adding both sides by [tex]\frac{12}{5}[/tex]
[tex]2x+6+\frac{12}{5} =\frac{24x}{5} -\frac{12}{5}+\frac{12}{5}\\ \\ 2x+\frac{42}{5} =\frac{24x}{5}[/tex]
Subtracting both sides by [tex]2x[/tex]
[tex]2x-2x+\frac{42}{5} =\frac{24x}{5} -2x\\ \\ \frac{42}{5} =\frac{24x-10x}{5} \\ \\ \frac{42}{5} =\frac{14x}{5} \\ \\[/tex]
By cross multiplication:-
[tex]5\times14x=5\times42\\ \\ 70x=210\\ \\[/tex]
By diving both sides by 70
[tex]x=3[/tex]
Now, substituting the value:-
The length = [tex]6x-3[/tex] cm
= [tex]6\times3-3=18-3=15\ cm[/tex]
The width = [tex]2x+6[/tex] cm
= [tex]2\times3+6=6+6=12\ cm[/tex]
Thus, length and width of canvas are 15 cm and 12 cm.
