#### Question

# The length of the top of a table is 6m greater than the width. The area is 91m^2. Find the dimensions of the?

The length of the top of a table is 6m greater than the width. The area is 91m^2. Find the dimensions of the table.

the width of the table is --------- m

the length of the table is --------m

#### Answer

a = lw

91 = (6 + w)w

91 = w^2 + 6w

0 = w^2 + 6w - 91

0 = (w + 13)(w - 7)

w = - 13 or w = 7

we can not have a negative length so w = 7 and l = 6 + w = 6 + 7 = 13

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x(x+6)=91

x^2+6x-91=0

x- width; x+6 length

x=-13; x= 7 But x>0 because it's a side of a rectangle

=> x=7 m

x+6=7+6=13 m

let width = x

length = x + 6

x(x + 6) = 91m^2

x^2 + 6x - 91 = 0

(x - 7)(x + 13)= 0

x = 7 or x = - 13

It can't be a minus so x = 7

Width = 7

length = 7 + 6 = 13

(x)(x+6)=91

x^2+6x-91=0

(x+13)(x-7)=0 x=7 x=-13 not acceptable

length =7+6=13

Let the length of the table be denoted by L.

Let the width of the table be denoted by W.

By given: L = W + 6.

Area table = L*W = (W + 6)*W = W^2 + 6W = 91.

W^2 + 6W = 91

W^2 + 6W - 91 = 0

(W - 7)(W + 13) = 0

W = 7 m (accepted).

W = - 13 m (rejected).

L = W + 6 = 7 + 6 = 13 m.

Then, the width of the table is 7 m and the length of the table is 13 m.

GOD bless you...