Question

10 in the diagram below, a rectangle is formed using the side lengths of two different squares. adef is a square with area measuring 162 is a square with area measuring 25 square units. 10a which three of the following expressions represent the area of rectangle abcd? lets try that again. $sqrt{162} cdot sqrt{25}$ $162 cdot sqrt{25}$ $9sqrt{2} cdot 5$ $sqrt{162} cdot 5$ $9sqrt{2} cdot 25$

Explanation:

Step1: Find side length of square ADEF

The area of square ADEF is 162, so side length \( AD = \sqrt{162} = \sqrt{81\times2} = 9\sqrt{2} \).

Step2: Find side length of square ABCH

The area of square ABCH is 25, so side length \( AB = \sqrt{25} = 5 \).

Step3: Area of rectangle ABCD

Area of rectangle is length × width, so \( \text{Area} = AD \times AB = \sqrt{162} \times \sqrt{25} = 9\sqrt{2} \times 5 = \sqrt{162} \times 5 \).

Answer:

\(\boldsymbol{\sqrt{162} \cdot \sqrt{25}}\), \(\boldsymbol{9\sqrt{2} \cdot 5}\), \(\boldsymbol{\sqrt{162} \cdot 5}\)