If the perimeter of a rectangular garden plot is 34 feet and its area is 60 sq. ft..?

Question

What is the length of each of the longer sides?

How do you get the conclusion?

Answer 1

Ok, here is what you know:

2a + 2b = 34; and a x b = 60 ft^2

So, starting with the first fact, simplify it:

2a + 2b = 34
2(a + b) = 34
a+b = 17

So you need two numbers that add up to 17 and multiply to make 60. Make a list:

1 and 16
2 and 15
3 and 14
4 and 13
5 and 12 <
6 and 11
7 and 10

5x12= 60, so those are your sides. The long sides are 12, short sides are 5.

Hope this helps!

Answer 2

You have -:

2x + 2y = 34 (Perimeter)
and
xy = 60 (Area)

You need to satisfy both equations.....

Factors of 60 are-:
1) 10 and 6
2) 12 and 5
3) 15 and 4
4) 20 and 3
5) 30 and 2

We can see that only one of these satisfy's both equations.....and that is number 2 -:

2 x 12 + 2 x 5 = 34 (Perimeter)

12 x 5 = 60 (Area)

Hence the length of the longer side is 12 feet.

Answer 3

Let 'l'& 'b' represent the longer and shorter sides of the rectangle. Then,

2(l + b) = 34 ---(1) and
l x b = 60 ---(2)
Hence b = 60/l. substitute this value of b in (1) to get
2(l+60/l) = 34
The equation reduces to a quadriatic equation on multiplication of all the terms with 'l' and it can be solved for 'l' to give the length of the longer side.

Answer 4

34 ft total length of all four sides.

Length x's Width = 60sq ft.

5ft x's 12ft = 60 ft.

Trial & error

Two sides are 5 ft & two sides are 12 ft.

5 x's 12 = 60

5 + 5 [two of the sides] + 12 + 12 [other two sides] = 34

Answer 5

area=length times width
therefore 60 =length times width
width=60/length

perimeter=2length + 2width
therefore expressing width in terms of length perimeter=2L+2(60/L)
P=2L+120/L
34=2L+120/L
therefore L=12

A=L times W
60=12 times W
W=5

the length of the longer sides is 12ft