Question

The width of a rectangle is 8 less than twice its length. If the area of the rectangle is 150 cm², what is thelength of the diagonal?Give your answer to 2 decimal places.​

Answer 1

The length of the rectangle's diagonal is calculated by first finding the rectangle's length and width using algebraic equations, then applying the Pythagorean theorem and rounding the result to two decimal places.

Step-by-step explanation:

The width of a rectangle is 8 less than twice its length. Given the area of the rectangle is 150 cm², we need to find the length of the diagonal. We can use algebra to find the length and width of the rectangle, and then apply the Pythagorean theorem to calculate the length of the diagonal.

Let the length of the rectangle be L. Then, the width, W, is 2L - 8. Since area A is length times width, A = L × W, we can set up the equation:

150 = L × (2L - 8)

Rearranging and solving this quadratic equation will give us the value of L. After finding the length L, we find the width W = 2L - 8. Finally, we can calculate the diagonal D using the Pythagorean theorem:

D = √(L² + W²)

The diagonal length will then be rounded to two decimal places, as required.