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

15 cm by 12 cm.

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
`(4)/(5)` of the length.

`2x+6=(4)/(5) (6x-3)\\ \\ 2x+6=(4)/(5)*6x-(4)/(5)*3\\ \\ 2x+6=(24x)/(5) -(12)/(5) \\ \\`

Adding both sides by
`(12)/(5)`

`2x+6+(12)/(5) =(24x)/(5) -(12)/(5)+(12)/(5)\\ \\ 2x+(42)/(5) =(24x)/(5)`

Subtracting both sides by
`2x`

`2x-2x+(42)/(5) =(24x)/(5) -2x\\ \\ (42)/(5) =(24x-10x)/(5) \\ \\ (42)/(5) =(14x)/(5) \\ \\`

By cross multiplication:-

`5*14x=5*42\\ \\ 70x=210\\ \\`

By diving both sides by 70

`x=3`

Now, substituting the value:-

The length =
`6x-3` cm

=
`6*3-3=18-3=15\ cm`

The width =
`2x+6` cm

=
`2*3+6=6+6=12\ cm`

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