Question

Help with this questions please!



math

Answer 1

Let length and breadth of rectangle be x metres and y metres respectively.

xy = 27 ---- eqn 1

x = 2y-3 ---- eqn 2

Sub eqn 2 into eqn 1:

(2y-3) × y = 27

2y² - 3y = 27

2y² - 3y - 27 = 0

(y+3)(2y-9) = 0

y+3=0 or 2y-9=0

y=-3 (rejected) 2y=9

y=4.5

Sub y=4.4 into eqn 2:

x = 2(4.5) - 3

= 6

Hence,

length of rectangle = x metres

= 6m

breadth of rectangle = y metres

= 4.5m

Answer 2

Explanation:

`area \: of \: rectangle = length * \: width`

Given

`l = 2w - 3`

using this

`area = l * w = (2w - 3)(w) = 27`

`2 {w}^(2) - 3w = 27`

`2 {w}^(2) - 3w - 27 = 0`

`2 {w}^(2) - 9w + 6w - 27 = 0`

`2w(w - 4.5) + 6(w - 4.5) = 0`

`(2w + 6)(w - 4.5) = 0`

`w = - 3 \: \: or \: \: w= 4.5`

Since size cannot be negative therefore

`w = 4.5cm`

`l = 2w - 3 = 9 - 3 = 6`

Hence length of the rectangle=6m

width of the rectangle=4.5m