GKADE 7 matiemATio SPEED TCST The diagenal of a rectangular piece of Home science project is 2.5 m . If the width of th piece of cloth is 1.5 m , what is the area of the cleth in square metres?

To find the area of the rectangular piece of cloth, we first need to determine its length using the given diagonal and width. We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides (the width and the length). Let: - \( d \) = diagonal = 2.5 m - \( w \) = width = 1.5 m - \( l \) = length (unknown) According to the Pythagorean theorem: \[ d^2 = w^2 + l^2 \] Substituting the known values: \[ (2.5)^2 = (1.5)^2 + l^2 \] Calculating the squares: \[ 6.25 = 2.25 + l^2 \] Now, subtract \( 2.25 \) from both sides: \[ 6.25 - 2.25 = l^2 \] \[ 4 = l^2 \] Taking the square root of both sides: \[ l = 2 \text{ m} \] Now that we have both the width and the length, we can calculate the area \( A \) of the rectangle: \[ A = l \times w \] Substituting the values: \[ A = 2 \text{ m} \times 1.5 \text{ m} = 3 \text{ m}^2 \] Thus, the area of the cloth is **3 square metres**.