Question

What are the dimensions of the rectangle (the length and width)?
You are given a rectangle. Its thin.

Information about rectangle:
Surface Area = 40 mm^2
Perimeter = 28 mm

What are the dimensions of the rectangle (the length and width)?
Please show the steps and the length and width as separate steps please

Answer 1

Answer:

4 and 10

Step-by-step explanation:

surface area means the length and the width of the rectangle add up to 40mm².

Since the perimeter is 28mm, it means 2L (2 length) + 2W (2 width) = 28mm.

1L + 1W = 14mm

1L x 1W = 40mm²

Factors of 40:

1 x 40

2 x 20

4 x 10

8 x 5

Since 4 & 10 is the only pair that adds up to 14, this is our answer.

Hope you found this helpful!

Answer 2

Step-by-step explanation:

length = l, and width = b

Step 1. let's try to get the value of length and breadth with given surface area

formula of surface area is l*b

lb= 40 --- eq1

Step 2.

formula of perimeter of rectangle

= 2(l+b)

2(l+b)=28

l+b=14 ----eq2

put the value of b from eq2 to eq1

we will get

l(14-l) = 40

$- {l}^{2} + 14l = 40$

${l}^{2} - 14l + 40 = 0$

now solve this quadratic equation,

${l}^{2} - 10l - 4l + 40 = 0$

$l(l - 10) - 4(l - 10) = 0$

$(l - 4)( l- 10) = 0$

so length comes out to be 4 or 10

Length and width will be (4,10) or (10,4).

HOPE IT HELPS

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