Answer:
The height of the painting is 28.7525 in and the width is 23.7425 in
Step-by-step explanation:
Let
x -----> the height of the painting
y -----> the width of the painting
we know that
The perimeter of the painting is
[tex]P=2(x+y)\\P=104.99\ in[/tex]
so
[tex]104.99=2(x+y)[/tex] ----> equation A
[tex]x=y+5.01[/tex] ----> equation B
substitute equation B in equation A and solve for y
[tex]104.99=2(y+5.01+y)[/tex]
[tex]52.495=2y+5.01[/tex]
[tex]2y=52.495-5.01[/tex]
[tex]y=23.7425\ in[/tex]
Find the value of x
[tex]x=23.7425+5.01=28.7525\ in[/tex]
therefore
The height of the painting is 28.7525 in and the width is 23.7425 in
The length and width of the painting are 23.74in and 28.75in respectively
Data;
The formula of perimeter of a rectangle is given as
[tex]P = 2(l+w)\\[/tex]
Let's substitute the values and solve
[tex]P = 2((y+5.01) + y)\\104.99 = 2(y+5.01+y)\\104.99 = 2(2y+5.01)\\104.99 = 4y + 10.02\\4y = 104.99 - 10.02\\4y = 94.97\\\frac{4y}{4} = \frac{94.97}{4} \\ y = 23.74[/tex]
The width is 23.74in and the length would be
[tex]23.74+5.01 = 28.75in[/tex]
The length and width of the painting are 23.74in and 28.75in respectively
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