Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

ABCD is a rectangle with AC=20 and AB=2BC. What is the area of rectangle ABCD?

Sagot :

Lilith
[tex]AC= 20 , \ AB=2BC \\\\ Pythagorean\ theorem,\ we \ have : \\ \\ |AC|^2 = (2|BC|)^2+ |BC|^2 \\ \\20^2 = 4|BC| ^2+ |BC|^2 \\ \\400 =5|BC|^2\ \ /:5[/tex]

[tex]|BC|^2=80 \\ \\|BC|=\sqrt{80}=\sqrt{16\cdot 5}=4\sqrt{5}\\ \\|AB|=2\cdot |BC| =2\cdot 4\sqrt{5}=8\sqrt{5}\\ \\Area = |AB|\cdot |A|\\ \\Area=8\cdot \sqrt{5}\cdot 4\cdot \sqrt{5}=32 \cdot 5 = 160 \\ \\ Answer : Area \ ABCD \ a \ rectangle = 160 [/tex]

View image Lilith
tadvisohil886
Let AB = 2x and BC be x.

By pythagoras theorum,

20² = x² + (2x)²

400 = x² + 4x²
400 = 5x²
80 = x²

x= √80 = 4√5 , thus, 2x = 8√5

Now, area = AB x AC

= 4√5 * 8√5

= 32 * 5

= 160

Thus, the area of rectangle ABCD is 160 units
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.