Justin's Question about Rectangle in Facebook

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In summary, Justin is new to geometry and is struggling to solve an equation given by his teacher. The equation involves finding the dimensions of a new rectangle, which is 6 units larger on each side and has an area 156 greater than the original rectangle. By setting up equations for the length, width, and area of the rectangle, Justin can solve for the dimensions of the new rectangle.
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Sudharaka
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Justin on Facebook writes:

hi.. I am new to geometry and my teacher gave me this equation and i have no idea how to solve it.. can u guys help me pls?

the length of a rectangle is three times as long as the width. If each side is increased by 6, the area of the new rectangle is 156 more than the area of the original rectangle. What are the dimensions of the new rectangle?
 
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Hi Justin, :)

Take the width of the rectangle as \(x\) and the length as \(y\). Then, \(y=3x\). The equation for the area of the rectangle being,

\[A=xy\]

Try to write an equation for the area of the new rectangle in terms of \(x,\,y\mbox{ and }A\). Notice that the new length is \(y+6\) and the width is \(x+6\). Then you can try to solve the three equations and find \(x\mbox{ and }y.\)
 

FAQ: Justin's Question about Rectangle in Facebook

What was Justin's question about rectangles on Facebook?

Justin's question was about finding the diagonal length of a rectangle given the length and width.

Why did Justin ask this question on Facebook?

Justin may have asked this question on Facebook to get help or clarification from his friends or followers who may have knowledge in geometry or mathematics.

Is this a common question in the field of science?

Yes, finding the diagonal length of a rectangle is a common question in the field of geometry and mathematics. It is a basic concept that is taught in schools and used in various applications.

What is the formula for finding the diagonal length of a rectangle?

The formula for finding the diagonal length of a rectangle is √(length² + width²). This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Are there any other methods for finding the diagonal length of a rectangle?

Yes, besides using the formula, the diagonal length of a rectangle can also be found by constructing a right triangle within the rectangle and using trigonometric functions such as sine, cosine, or tangent to find the length of the hypotenuse.

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