an architect wants to draw a rectangle with a diagonal of 13 inches.the length of the rectangle is to be 2 inches more thn twice the width.what dimensions should she make the triangle.

(a)set up an equation:

(b)solve the equation:

(c)write a sentence that answers the quation:

(a) Let's assume the width of the rectangle is x inches. According to the problem, the length of the rectangle is 2 inches more than twice the width, so it would be 2x + 2 inches.

(b) Now, since the diagonal of the rectangle is given to be 13 inches, we can use the Pythagorean theorem to set up the equation:

x^2 + (2x + 2)^2 = 13^2

Simplifying this equation will allow us to solve for x.

(c) After solving the equation, we find that the dimensions of the rectangle should be approximately x = 3.72 inches and 2x + 2 = 9.44 inches. Therefore, the architect should make the rectangle approximately 3.72 inches wide and 9.44 inches long.

(a) Let's set up an equation to solve the problem.

Let w represent the width of the rectangle. Since the length is 2 inches more than twice the width, the length would be (2w + 2).

Using the Pythagorean theorem: (width)^2 + (length)^2 = (diagonal)^2, we can write the equation as:

w^2 + (2w + 2)^2 = 13^2

(b) Now, let's solve the equation:

Expanding the equation:
w^2 + 4w^2 + 4w + 4 = 169

Combining the like terms:
5w^2 + 4w + 4 = 169

Rearranging the equation:
5w^2 + 4w - 165 = 0

Factoring the equation:
(5w - 33)(w + 5) = 0

Setting each factor equal to zero:
5w - 33 = 0 or w + 5 = 0

Solving for w:
5w = 33 or w = -5
w = 33/5 or w = -5

Ignoring the negative value, we have:
w = 33/5

Substituting the value of w into the equation (2w + 2) for the length:
Length = 2(33/5) + 2
Length = 66/5 + 10/5
Length = 76/5

(c) The dimensions of the rectangle should be approximately: width = 6.6 inches and length = 15.2 inches.

(a) To solve this problem, let's set up an equation based on the given information. Let's assume the width of the rectangle is "w" inches. According to the problem, the length of the rectangle is 2 inches more than twice the width. So, the length would be (2w + 2) inches.

(b) Now, we can use the Pythagorean Theorem to find the value of "w". The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.

Using this theorem, we can write the equation as:
w^2 + (2w + 2)^2 = 13^2

Simplifying the equation, we get:
w^2 + 4w^2 + 4w + 4 - 169 = 0
5w^2 + 4w - 165 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Either method will provide us with the value of "w", which is the width of the rectangle.

(c) The solution to the quadratic equation will give us the width of the rectangle. Once we have the width, we can calculate the length of the rectangle based on the given relationship.

Dia. = 13 In. = Hyp. of rt triangle.

Width=x In.=Ver. side of a rt triangle
Length = 2x+2 In. = Hor. side of rt triangle.

a. (2x+2)^2 + x^2 = 13^2.

b. 4x^2+8x+4 + x^2 = 169
5x^2 + 8x -165 = 0
Use Quadratic Formula:
X = 5 In.
X = -6.6 Not valid.

2x+2 = 2*5 + 2 = 12 In.