Mathematics: Cynthia besch wants to buy a rug for a room that is 23ft wide and 26ft long. She wants t ok leave a uniform strip of floor around the rug. She can only afford to buy 270 square feet of carpeting. What dimensions should the rug have?

Cynthia besch wants to buy a rug for a room that

Ответ:

128585

19.01.2022

Mathematics

$(15\times 18)\ ft$

Step-by-step explanation:

Given: Area of rug= 270 ft²

Cynthia besch wants to buy a rug for a room that is 23ft wide and 26ft long.

Let´s assume the uniform strip size of floor around rug be "x".

As given, Cynthia wants to leave a uniform strip of floor around the rug.

Considering the shape of rug as rectangle.

∴ Rug dimension will be $(23-2x)\times (26-2x)$

We know, area of rectangle= $width\times length$

Forming an equation for area of rug.

⇒ $270= (23-2x)\times (26-2x)$

Now solving the equation to find the dimension of rug.

$270= (23-2x)\times (26-2x)$

Using distributive property of multiplication.

⇒ $270= 598-46x-52x+4x^{2}$

⇒ $598-98x+4x^{2}= 270$

Subtracting both side by 270

⇒ $4x^{2}-98x+328= 0$

using quadratic formula to solve the equation.

Formula: $\frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}$

∴ In the expression , we have a= 4, b= -98 and c= 328.

Now, subtituting the value in the formula.

= $\frac{-(-98)\pm \sqrt{-98^{2}-4(4\times 328) } }{2\times 4}$

= $\frac{98\pm \sqrt{9604-4(1312) } }{8}$

Opening parenthesis.

= $\frac{98\pm \sqrt{9604-5248 } }{8}$

= \frac{98\pm \sqrt{4356}}{8}

We know 66²=4356 and √a²=a or -a

= $\frac{98\pm 66}{8}$

= $\frac{98+66}{8}\ or \ \frac{98-66}{8}$

= $20.5 \ or\ 4$

∴ Value of x will be either 20.5 ft or 4 ft

Ignoring decimal value, therefore taking value of x as 4 ft.

Subtituting the value of x to find the dimension of rug.

Width of rug= (23-2x)

⇒ Width of rug= $23- 2\times 4$

⇒ Width of rug= $23-8= 15\ ft$

Next, Length of rug= (26-2x)

⇒ Length of rug= $26-2\times 4$

⇒ Length of rug= $26-8= 18\ ft$

Hence, dimension of rug is $(15\times 18)\ ft$

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Ответ:

mimi5937

05.01.2020

Mathematics

Be able to identifypostulates used toprove the two trianglesare similar.
-Angle-Angle (AA) Similarity Postulate
-Side-Side-Side (SSS) Similarity Theorem
-Side-Angle-Side (SAS) Similarity Theorem

Be able to describe how they are applied.
-AA Postulate - If two angles of one triangle are congruent to two angles of another, then the triangles must be similar.
-SSS Theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar.
-SAS Theorem - If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles must be similar.
those are the first two parts good luck on the rest of it, have a nice day

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Cynthia besch wants to buy a rug for a room that is 23ft wide and 26ft long. She wants t ok leave a uniform strip of floor around the rug. She can only afford to buy 270 square feet of carpeting. What dimensions should the rug have?

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