MATHEMATICS HIGH SCHOOL

A rectangle has perimeter 26 cm, and the length and width are both whole numbers. What is the greatest possible area this rectangle may have in square cm?

Answers

Answer 1

Answer:

The length should be 7 while the breadth should be 6 to maximize the area.

Perimeter of the Rectangle

The perimeter of the rectangle is twice the sum of its length and breadth.

$\rm{Perimeter = 2(length +breadth)$

Area of the rectangle

the area of the rectangle is given as the product of its length and its breadth.

$\rm{Area ={length* breadth$

Given to us

Permeter = 26 cm

Perimeter

$\rm{Perimeter = 2(length +breadth)$

$26 = 2(length +breadth)$

$13=(length +breadth)$

Area of the rectangle

As we know that the area is given as the product of length and breadth. so, we need to find those numbers whose sum is 13. while their product gives us the maximum area.

Therefore, for the area to be maximum the length and breadth should be maximum.

$1 * 12 = 12\n2* 11 = 22\n3* 10 = 30\n4* 9 = 36\n5* 8 = 40\n6* 7 = 42$

Thus, the length should be 7 while the breadth should be 6 to maximize the area.

Learn more about Rectangles:

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Answers

1/3 + 2/5 • 2/3

2 • 2 = 4
5 • 3 = 15

1/3 = 5/15

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the Kelly family bought a new pet rabbit. They want to build an enclosure outside so it has lots of room to roam. They have 30 feet of leftover lumber to use. Find the length and width of the enclosure if the length is to be 4fteet longer than twice the width.

Answers

assume that since this is a simple math problem and they only mentioned legnth and witdth,
assume a perfect rectangle

so assuming they use all the lumber
30=perimiter
perimiter=legnth around=legnth+legnth+with+width

30=2legnth+2width
undistribute
30=2(legnth+width)
divide by 2
15=legnth+width
legnth is 4 more than 2width
legnth=4+2width
subsitute
15=legnth+width
15=4+2width+width
subtract 4
11=2width+width
divide by 3
11/3=width

legnth=4+2width
legnth=4+2 times (11/3)
lefnth=4+22/3
4=12/3
legnth=12/3+22/3
legnth=34/3 feet=11 and 1/3 foot

width=11/3=3 and 2/3

legnth=11 and 1/3 foot
width=3 and 2/3 foot

The sum of 6 consecutive integers is 387. what is the sixth number in this sequence?

Answers

6 consecutive integers : x, x + 1, x + 2, x + 3, x + 4, x + 5

the sum is 387...
x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 387...combine like terms
6x + 15 = 387
6x = 387 - 15
6x = 372
x = 372/6
x = 62

the 6th number, which is x + 5 is : 62 + 5 = 67 <==

What is the ratio 35 to 56 written as a fraction in lowest terms?