Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The diagram shows two squares constructed on the sides of a rectangle. Write an expression for the area of Square C in terms of the areas of Square A and Rectangle B. Then simplify to find the area. (N RN.1.1-2 HELP PLSSS

The Diagram Shows Two Squares Constructed On The Sides Of A Rectangle Write An Expression For The Area Of Square C In Terms Of The Areas Of Square A And Rectang class=

Sagot :

ChoiSungHyun

Step-by-step explanation:

Since area of Square A = 7 ft²,

Side length of Square A = √7 ft.

Length of Rectangle B = √7 ft

Width of Rectangle B = 4/√7 ft

Hence Area of Square C

= (4)² / (√7)² ft² = 16/7 ft².

The area of Square C is the square of the height of the Rectangle B.

Correct responses:

  • [tex]\underline{Area \ of \ square \ C = \dfrac{\left(Area \ of \ Rectangle \ B \right)^2}{Area \ of \ Square \, A} }[/tex]

  • [tex]Area \ of \ square \ C = \underline{\dfrac{16}{7}} \, ft.^2[/tex]

Methods used for finding the area of Square C

The given area of square A = 7 ft.²

The given area of rectangle, B = 4 ft.²

Let s represent the side length of square C and let S represent the side length of square A, we have;

Area of rectangle B = S × s = S·s

Area of square A = S × S = S²

Area of square C = s × s = s²

[tex]\mathbf{\dfrac{(Area \ of \ rectangle \ B)^2}{Area \ of \ square \ A } } = \dfrac{\left(S \cdot s \right)^2}{S^2} = \dfrac{S^2 \cdot s^2}{S^2} = s^2 = Area \ of \ square \ C[/tex]

Therefore, the expression for the area of Square C in terms of the area

of Square A and Rectangle B is presented as follows;

  • [tex]\underline{Area \ of \ Square \ C = \dfrac{ \left (Area \ of \ rectangle \ B \right)^2}{\left(Area \ of \ square \ A\right)}}[/tex]

Which gives;

  • [tex]\underline{Area \ of \ square \ C = \dfrac{\left(4 \, ft.^2 \right)^2}{7 \, ft.^2}}[/tex]

By simplification, we have;

[tex]\mathbf{\dfrac{\left(4 \, ft.^2 \right)^2}{7 \, ft.^2}} = \dfrac{16}{4} \, ft.^2[/tex]

  • [tex]Area \ of \ square \ C = \underline{ \dfrac{16}{7}} \, ft.^2[/tex]

Learn more about squares and rectangles here:

https://brainly.com/question/2288475

https://brainly.com/question/14044544

https://brainly.com/question/8428727

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.