Question

Amanda uses a rectangular canvas for a panting. The length is 6x-3 centimeters The width is 2x+6 centimeters,and is 4/5of the length .What are the dimensions of the canva

Answer 1

Answer:

15 cm by 12 cm.

Step-by-step explanation:

Given:

Amanda uses a rectangular canvas for a panting.

The length is $6x-3$ centimeters.

The width is  $2x+6$ centimeters, and is 4/5 of the length .

Question asked:

.What are the dimensions of the canvas ?

Solution:

As given that the width is $\frac{4}{5}$ of the length.

$2x+6=\frac{4}{5} (6x-3)\\ \\ 2x+6=\frac{4}{5}\times6x-\frac{4}{5}\times3\\ \\ 2x+6=\frac{24x}{5} -\frac{12}{5}$

Adding both sides by $\frac{12}{5}$

$2x+6+\frac{12}{5} =\frac{24x}{5} -\frac{12}{5}+\frac{12}{5}\\ \\ 2x+\frac{42}{5} =\frac{24x}{5}$

Subtracting both sides by $2x$

$2x-2x+\frac{42}{5} =\frac{24x}{5} -2x\\ \\ \frac{42}{5} =\frac{24x-10x}{5} \\ \\ \frac{42}{5} =\frac{14x}{5}$

By cross multiplication:-

$5\times14x=5\times42\\ \\ 70x=210$

By diving both sides by 70

$x=3$

Now, substituting the value:-

The length = $6x-3$ cm

                  = $6\times3-3=18-3=15\ cm$

The width = $2x+6$ cm

                 = $2\times3+6=6+6=12\ cm$

Thus, length and width of canvas are 15 cm and 12 cm.