Answer: [tex]26\ cm[/tex]
Step-by-step explanation:
The perimeter of a rectangle can be calcualated with this formula:
[tex]P=2l+2h[/tex]
Where "l" is the lenght and "h" is the height.
The area of a rectangle can be found with this formula:
[tex]A=lh[/tex]
Where "l" is the lenght and "h" is the height.
In this case we know that:
[tex]A=40\ cm^2[/tex]
Therfore, we can susbsitute them into [tex]A=lh[/tex] and solve for "h" in order to find its value:
[tex]40=(h+3)h\\\\40=h^2+3h\\\\h^2+3h-40=0[/tex]
Find two number whose sum is 3 and whose product is -40. These are -5 and 8. Then, factorizing, we get:
[tex](h-5)(h+8)=0\\\\h_1=5\\\\h_2=-8[/tex]
The positive value is the height. Then:
[tex]h=5\ cm[/tex]
Since the length is 3 centimeters greater than its height, we get that this is: Then:
[tex]l=5\ cm+3\ cm\\\\l=8\ cm[/tex]
Substituting values into [tex]P=2l+2h[/tex], we get that the perimeter is:
[tex]P=2(8\ cm)+2(5\ cm)\\\\P=26\ cm[/tex]
The perimeter of a rectangle : 26 cm
There are several properties possessed by rectangular shapes, namely:
There are two rectangular shapes namely square and rectangle
Square if all sides are the same length
The formula used in rectangular is:
Rectangle
Area (A) = l x h
h = height
l = length
Square
Area (A) = a²
a = length of side
Rectangle
Perimeter = P = 2 (l + h)
h = height
l = length
Square
P = 4 x a
a = length of side
length is 3 cm greater than its height
we translate this sentence into Algebraic expressions
l = 3 + h
Then :
Area = l x h
Area = (3+h)h
40 = 3h+h²
h²+3h-40 = 0
factorizing ⇒ (h-5)(h+8)=0
h1 = 5 and h2 = -8
we take positive values h1 = 5
l = 3 + h
l = 3 + 5
l = 8
the perimeter of a rectangle :
[tex]\rm P=2(l+h)\Rightarrow P=2(8+5)\\\\P=2(13)\Rightarrow P=\boxed{\bold{26}}[/tex]
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