Find the length of the diagonal of a rectangular garden measuring 6 m by 8 cm. Assume dimensions are 6m and…

Question

Find the length of the diagonal of a rectangular garden measuring 6 m by 8 cm. Assume dimensions are 6m and 8m.

ScanSolve AI Tutor · Accepted Answer

The problem asks to find the length of the diagonal of a rectangular garden that measures 6 m by 8 cm. There appears to be a unit inconsistency (meters and centimeters). Assuming the diagram is correct and the dimensions are 6 m and 8 m, we will proceed with that assumption. If the 8 cm is correct, please clarify.

Identify the dimensions of the rectangle.
The length of the rectangle is $8 \text{ m}$ and the width is $6 \text{ m}$ . The diagonal of a rectangle forms the hypotenuse of a right-angled triangle with the length and width as its legs.
Apply the Pythagorean theorem.
Let $d$ be the length of the diagonal, $l$ be the length, and $w$ be the width. The Pythagorean theorem states:
$d^2 = l^2 + w^2$
Substitute the given values into the formula.
$d^2 = (8 \text{ m})^2 + (6 \text{ m})^2$ $d^2 = 64 \text{ m}^2 + 36 \text{ m}^2$ $d^2 = 100 \text{ m}^2$
Solve for $d$ .
$d = \sqrt{100 \text{ m}^2}$ $d = 10 \text{ m}$
The length of the diagonal is $\text{10 m}$ .

Find the length of the diagonal of a rectangular garden measuring 6 m by 8 cm. Assume dimensions are 6m and 8m.

Answer

Step-by-step solution

Identify the dimensions of the rectangle.

Apply the Pythagorean theorem.

Substitute the given values into the formula.

Solve for $d$ .

Try one yourself

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More Mathematics Questions

Find the length of the diagonal of a rectangular garden measuring 6 m by 8 cm. Assume dimensions are 6m and 8m.

Answer

Step-by-step solution

Identify the dimensions of the rectangle.

Apply the Pythagorean theorem.

Substitute the given values into the formula.

Solve for ddd.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Solve for $d$ .