Question

the length of a rectangle is 5 cm more than its width and the area is 50cm2 find the legth, width, and the perimeter

Answer 1

the length of a rectangle is 5 cm more than its width and the area is 50cm2 find the length, width, and the perimeter

L = W + 5 (5 cm more than its width)

Area = W * L

Substitute Area = 50 and L = W + 5

50 = W ( W+5)

Distributive property

50 = W^2 + 5W

Subtract 50 from both sides

0 = W^2 + 5W - 50

Re-write

W^2 + 5W - 50 = 0

Factor

(W + 10)(W - 5) = 0

W + 10 = 0; W = -10

W - 5 = 0; W = 5

Dimension cannot be negative so W = 5 cm

L = 5 + 5 = 10 cm

Double check: A = 5 x 10 = 50 cm^2

Perimeter = 2(L + W)

Perimeter = 2(5 + 10)

Perimeter = 2(15)

Perimeter = 30 cm

Answer

L = 10 cm

W = 5 cm

P = 30 cm

Hope that helps

Answer 2

Let the Width be x cm

Then the length which is 5cm more than width must be (x+5) cm

Using the formula for the area = length* width

x(x+5) =50

`x^2+5x =50` (Distribute x on the parenthesis )

`x^2+5x-50 =0` (subtract 50 )

`(x+10) (x-5) =0` (Factor)

`x-5=0\\x+10=0`

we get

`x=5` (Not x=-10 because negative side length not possible)

Width = 5 cm

Length = 5+5= 10 cm

Perimeter = 2(Length + width)

So

Perimeter = 2(10+5)

Perimeter = 2*15=30 cm