Question

Find the perimeter of a rectangle whose length is 3 cm greater than its height, and whose area is 40 cm².

Answer 1

Answer: $26\ cm$

Step-by-step explanation:

The perimeter of a rectangle can be calcualated with this formula:

$P=2l+2h$

Where "l" is the lenght and "h" is the height.

 The area of a rectangle can be found with this formula:

$A=lh$

Where "l" is the lenght and "h" is the height.

In this case we know that:

$A=40\ cm^2$

Therfore, we can susbsitute them into $A=lh$ and solve for "h" in  order to find its value:

$40=(h+3)h\\\\40=h^2+3h\\\\h^2+3h-40=0$

Find two number whose sum is 3 and whose product is -40. These are -5 and 8. Then, factorizing, we get:

$(h-5)(h+8)=0\\\\h_1=5\\\\h_2=-8$

The positive value is the height. Then:

$h=5\ cm$

Since the length is 3 centimeters greater than its height, we get that this is: Then:

$l=5\ cm+3\ cm\\\\l=8\ cm$

Substituting values into $P=2l+2h$, we get that the perimeter is:

$P=2(8\ cm)+2(5\ cm)\\\\P=26\ cm$

Answer 2

The perimeter of a rectangle : 26 cm

Further explanation

There are several properties possessed by rectangular shapes, namely:

• 1. each angle is equal and is a right angle
• 2. the diagonals intersect and divide each other equally
• 3. the opposite sides have the same length

There are two rectangular shapes namely square and rectangle

Square if all sides are the same length

The formula used in rectangular is:

• 1.Area

Rectangle

Area (A) = l x h

h = height

l = length

Square

Area (A) = a²

a = length of side

• 2. perimeter

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 :

$\rm P=2(l+h)\Rightarrow P=2(8+5)\\\\P=2(13)\Rightarrow P=\boxed{\bold{26}}$

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