Answer:
1. width = 4 inches length = 13 inches
2. 225 m²
Step-by-step explanation:
1. So we know there are two sides and one side is 9 more than the other.
We let one side be x as we don't know what the number is. The other side is x+9 as its 9 more than the first side but we don't what that is either.
We know the area of a rectangle is A = bh.
The two sides are x and x+9
so, x(x+9) = 52
x² + 9x = 52
x² + 9x - 52 = 0
x² + 13x - 4x - 52 = 0
x(x+13) -4(x+13) = 0
(x-4)(x+13) = 0
x = 4 x = 13
The answer is x = 4 because you can't have x = -13 as negative lengths don't exist.
So if one side is x and the other side is x+ 9. Then plugging in 4 to both gets us, 4 and 13 as the dimensions.
The length is 9 more than width so,
length = 13 inches and width = 4 inches.
2. We know the area of a rectangle is A = bh.
One side is x + 10 and the other is x+15
Area is 750.
(x+10)(x+15) = 750
x²+15x+10x+150 = 750
x²+15x+10x-600 = 0
x²+25x-600 = 0
(x+40)(x-15) = 0
x = 15 as we can't have x = -40 because negative distance does not exist.
The bistro has sides x and x.
So the area is x * x.
15 * 15 = 225 m².
