Using the Pythagorean theorem, we know that:
diagonal² = side1² + side2²
So in this case:
(x+8)² = x² + (x+7)²
Expanding the parentheses:
x² + 16x + 64 = x² + x² + 14x + 49
Simplifying:
x² + 2x - 15 = 0
Factoring:
(x+5)(x-3) = 0
Therefore, x = -5 or x = 3. Since a negative length is nonsensical, we have x = 3.
Now we can calculate the area of the floor:
Area = length x width = xm(x+7)m = 3m(10)m = 30m²
So the value of x is 3 metres and the area of the floor is 30 square metres.
The sides of a rectangular floor are xm and (x+7)m the diagonal is (x+8)m. Calculate in metres the value of x and the area of the floor
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