Question

A garden is currently 4 meters wide and 7 meters long. If the area of the garden is to be doubled by increasing the width and length by the same number of meters, find the new dimensions of the garden, rounded to the nearest tenth.

Answer 1

Given,
Width(w) = 4 meters
Length (L) = 7 meters
So, area is 4*7 = 28 Meters sq
Area of garden is to be doubled so area is 2* 28 = 56 Sq meters
And For that length and width should increase by same number so let it be x
so,
(4+x)*(7+x)= 56
By solving that u get ,
X is approximately equals to 2.13,
so we can say it as 2.

Answer 2

the new length of rectangular garden x + 7 = 2 + 7 = 9 meters

The new width of the rectangular garden x + 4 = 2 + 4 =6 meters.

The new area of rectangular garden 56 meters

What is Rectangular?

A rectangular is "2D shape that has 4 sides, 4 corners and 4 right angle".

According to the question,

wide of rectangular garden = 4meters

Length of rectangular garden = 7meters.

Formula for Area of Rectangle = length × breadth.

Area of Rectangle = 7 × 4 = 28meters

The area of the Rectangular garden is to be doubled by increasing the width and length by the same number of meters.

Area of Rectangle = 56meters

(4+x)*(7+x) = 56 meters

28 + 4x + 7x + $x^{2}$ =56

$x^{2}$ + 11x+ 28 -56 =0

$x^{2}$ +11x - 28=0

using quadratic equation, $\frac{-b ± \sqrt({b^2}-4ac) }{2a}$  where a=1, b = 11, c =-28

= $\frac{-11±\sqrt{((11)^2-4(1)(28)} }{2(1)}$

x = $\frac{(-11)+\sqrt{233} }{2}$$\frac{(-11)+\sqrt{233} }{2}$ = 2.132 ≈ 2

x = $\frac{(-11)-\sqrt{233} }{2}$  = -(13.132)      [Neglect negative value]

Area of rectangular garden is doubled so the dimension of length and width is increased by '2'. So add '2' to length and width to get new dimensions.

Hence, the new length of rectangular garden x + 7 = 2 + 7 = 9 meters

The new width of the rectangular garden x + 4 = 2 + 4 =6 meters.

The new area of rectangular garden 56 meters

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