Respuesta :
Answer:
length = 15 cm
width = 12cm
Step-by-step explanation:
The length of the rectangular canvas = (6x - 3) cm
The width = (2x + 6) cm
The width is 4/5 of the length which can be represented as follows
4/5 × (6x - 3) = 4/5(6x - 3)
(24x/5 - 12/5) cm
The width is also 2x + 6
24x/5 - 12/5 = 2x + 6
collect like terms
24x/5 - 2x = 6 + 12/5
(24x - 10x)/5 =(30 + 12) /5
14x/5 = 42/5
cross multiply
14x × 5 = 5 × 42
70x = 210
divide both sides by 70
x = 210/70
x = 3
length
6x - 3
6(3) - 3
18 - 3 = 15 cm
width
2x + 6
2(3) + 6
6 + 6
12 cm
[tex]15\,cm,12\,cm[/tex]
A rectangle is a parallelogram in which each of the angles is a right angle.
Length of a rectangular canvas [tex]=(6x-3)\,cm[/tex]
Width of a rectangular canvas [tex]=(2x+6)\,cm[/tex]
Also, the width is [tex]\frac{4}{5} [/tex] of the length.
Therefore,
[tex]2x+6=\frac{4}{5}\left ( 6x-3 \right )[/tex]
[tex]10x+30=24x-12[/tex]
[tex]14x=42[/tex]
[tex]x=3[/tex]
So,
Length [tex]=6(3)-3[/tex]
[tex]=15\,cm[/tex]
Width [tex]=2(3)+6[/tex]
[tex]=12\,cm[/tex]
Dimensions are [tex]\boldsymbol{15\,cm,12\,cm}[/tex]
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