Question

Please help me and give an accurate answer

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Answer 1

first off, let's take a looksie at the counter hmmm, vertically it has sides of (2x) and 0.6 and (2x) and 0.6, and horizontally it has a side of (3x + 5) and 0.6, and we know if we add those rectangular areas, they add up to 23.28 m², so let's add them up

`(2x)(0.6)~~ + ~~(3x+5)(0.6)~~ + ~~(2x)(0.6)~~ = ~~23.28 \\\\\\ 1.2x~~ + ~~1.8x+3~~ + ~~1.2x~~ = ~~23.28\implies 4.2x+3=23.28 \\\\\\ 4.2x=20.28\implies \cfrac{42x}{10}=\cfrac{2028}{100}\implies 4200x=20280 \\\\\\ x=\cfrac{20280}{4200}\implies \boxed{x=\cfrac{169}{35}}`

now, well, let's take a peek at the "island" in the middle of the kitchen, hmm it has dimensions of (x-3) and (x-4), let's get its area

`(x-3)(x-4)\implies \stackrel{ F~O~I~L }{x^2-7x+12}\implies \left( \cfrac{169}{35} \right)^2 - 7\left( \cfrac{169}{35} \right)+12 \\\\\\ \cfrac{28561}{1225}-\cfrac{169}{5}+12\implies \cfrac{28561-14700+14700}{1225}\implies \cfrac{28561}{1225}\implies {\Large \begin{array}{llll} 23(386)/(1225) \end{array}}`

Answer 2

2 m²

Explanation:

Give a U-shaped counter with outside leg dimensions of (2x), center bridge outside dimension (3x+5), width 0.6 m, and area 23.28 m², you want the area of a rectangular island with dimensions (x-3) and (x-4).

Counter area

We can consider the counter area to be 3 rectangles of width 0.6 m and total length (2x) +(3x+5) +(2x) = 7x +5. Then the area will be ...

0.6(7x+5) = 4.2x +3 . . . . . . square meters

This area includes both 0.6 m square corners twice, so the actual counter area is ...

4.2x +3 -2(0.6²) = 23.28 . . . . . . square meters

4.2x = 21 . . . . . . . . . . . . . . . . subtract 2.28

x = 5 . . . . . . . . . . . . . . . . divide by 4.2

Island area

This makes the island area be ...

A = (x -3)(x -4) = (5 -3)(5 -4) = (2)(1)

A = 2

The area of the island is 2 square meters.