The side of a rectangular floor are x and (x+7).The diagonal is x+8.calculate in metres
a.the value of x
b.the area of the floor
well, the diagonal^2=x^2+(x+7)^2
(x+8)^2=x^2+(x+7)^2
mulltiply that out, solve for x
then for areas, multiply the two sides (x) and (x+7)
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a. Well, I'm not much of a mathematician, but let's give it a try. We can use the Pythagorean theorem to solve for x. According to the theorem, the square of the diagonal is equal to the sum of the squares of the two sides. So, we have (x+8)^2 = x^2 + (x+7)^2. Expanding and simplifying the equation gives us x^2 + 16x + 64 = x^2 + x^2 + 14x + 49. Combining like terms, we get 3x^2 + 2x - 15 = 0. Factoring or using the quadratic formula, we find that x = -3 or x = 5/3. However, since we are dealing with the measurement of a floor, we can safely ignore the negative solution. So, x = 5/3 or approximately 1.67 meters.
b. To find the area of the floor, we can simply multiply the length by the width. The length is x+7 and the width is x. So, the area would be (x+7)(x) = x^2 + 7x. Since we already found x to be 5/3 or 1.67 meters, we can plug that value in to get the area: (1.67)^2 + 7(1.67) = 2.78 + 11.69 = 14.47 square meters.
To find the value of x and the area of the floor, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, since the diagonal is the hypotenuse, we can use the equation: (x+8)^2 = x^2 + (x+7)^2.
Let's simplify this equation to find the value of x and calculate the area of the floor.
a. Value of x:
Expanding the equation, we get:
x^2 + 16x + 64 = x^2 + x^2 + 14x + 49.
Combining like terms, we have:
2x^2 + 16x + 64 = 2x^2 + 14x + 49.
Simplifying further:
16x + 64 = 14x + 49.
Move the variables to one side and the constants to the other side:
16x - 14x = 49 - 64.
Simplifying again:
2x = -15.
Divide both sides by 2:
x = -7.5.
Therefore, the value of x is -7.5 meters.
b. Area of the floor:
To find the area of the floor, we multiply the lengths of the sides:
Area = x * (x+7).
Substituting the value of x we found earlier, we have:
Area = -7.5 * (-7.5 + 7).
Simplifying further, we get:
Area = -7.5 * -0.5.
Multiplying these values, we obtain:
Area = 3.75 square meters.
Therefore, the area of the floor is 3.75 square meters.