the with of a rectangle is 5m less than the lenth. the area is 66m^2. find the length.?

the width of a rectangle is 5m less than the length:
w+5 = l

A = l*w = 66

A = (w+5)*w = 66
A = (w+5)*w = w^2 + 5w = 66

w^2 + 5w - 66 = 0
Factor:
(w + 11)(w - 6) = 0
==> w = -11 or w = 6
Since length and width cannot be negative, we can disregard w=-11

So w=6 and l=w+5=6+5=11

the width of a rectangle is 5m less than the length:
w+5 = l

A = l*w = 66

A = (w+5)*w = 66
A = (w+5)*w = w^2 + 5w = 66

w^2 + 5w - 66 = 0
Factor:
(w + 11)(w - 6) = 0
==> w = -11 or w = 6
Since length and width cannot be negative, we can disregard w=-11

So w=6 and l=w+5=6+5=11

Hi,

Let length be l, and width be w.

The width of a rectangle is 5m less than the length.

w = l - 5

The area is 66m².

wl = 66


(l - 5)l = 66

l² - 5l - 66 = 0

(l - 11)(l + 6) = 0

Length = 11 cm

Hope this helps!

The width of a rectangle is 3 inches under its length. the component to the rectangle is 340 sq.? The width of a rectangle is 3 inches under its length. the component to the rectangle is 340 sq. inches. What are the size and width of the rectangle? length =X WIDTH = X-3 X(X-3)=340 x^2 -3x=340 x^2 -3x-340=0 (x-20)(x+17)=0 x=20 so the size is 20 and the width is 17 A. length = 20 inches, width = 17 inches B. length = 10 inches, width = 7 inches C. length = 17 inches, width = 14 inches D. length = 34 inches, width = 10 inches

The area of a rectangle is:

length x width = Area of rectangle.

Let's suppose you give a value of x to the length of the rectangle. And the width should be 5 m less than the length, so it should be (x - 5). Now, the area should be:

x (x-5) = 66
x(x) - x(5)=66 (distributive property)
x^2 - 5x = 66.

Now, you have a quadratic equation. Simply make it equal to zero.

x^2 - 5x - 66 = 0.

Now, you can solve this by two methods: factoring or by using the quadratic formula. Factoring is easier than quadratic formula, so I will use that method.

Factoring: Find two binomials that equal the quadratic equation.
( )( ) = x^2 - 5x - 66 = 0

When the coefficient of x^2 is 1, the first term of both binomials is x

(x ) (x ) =x^2 - 5x - 66 = 0

Find two numbers that their sum equals - 5 and their product equals -66. Those numbers are -11 and 5. Put them in the binomials next to the x.

(x + 5) (x - 11) = 0

Now, make the factors equal to 0. When you multiply both binomials, the answer should be 0 because one of them is 0.

x + 5 = 0
x - 11=0

Now, the answers...

x = - 5, x= 11.
because the length of a rectangle can't be a negative number, we discard that solution and the answer should be
11 m : length
5 m : width

Hope this helped.

let x = width
let x-5m= length
A=66m^2

A=L*W
A=x*(x-5)
66=x^2-5x
0=x^2-5x-66
0=(x-11)(x+6)

x-11=0
x=11

x+6=0
x=-6

it is impossible to have a negative measurement

so, the length is 11m

the width of a rectangle is 5m less than the length:
w+5 = l

A = l*w = 66

A = (w+5)*w = 66
A = (w+5)*w = w^2 + 5w = 66

w^2 + 5w - 66 = 0
Factor:
(w + 11)(w - 6) = 0
==> w = -11 or w = 6
Since length and width cannot be negative, we can disregard w=-11

So w=6 and l=w+5=6+5=11

x times (x-5) = 66
x^2 - 5x = 66
x^2 - 5x - 66 = 0

you can do the rest

W=L-5

A=L * W = 66
L * (L-5)=66
L^2-5L=66
L^2-5L-66=0
(L-11)(L+6)=0
L=11, L=-6

L cannot be -6, so L=11 W=6

let length = x
width is 5m less than the length, so x-5

area = length x width

so x(x-5) = 66
x^2 - 5x = 66
x^2 - 5x - 66 = 0
(x + 6)(x - 11) = 0
x = -6, 11

x can't be negative, so x = 11

therefore length is 11