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

Question

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

Answer 1

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.