Question

jose needs to enclose a rectangular section of his yard. the perimeter of the section is 27 feet, and the area? is 35 square feet ...find the length and width of the selection. let l=length and w-width write and equation for the perimenter... p=2(l w) then solve for w then write an equation for the area use the quadratic formula to solve for l

Answer 1

Part I: Let L = length of the section and let W = width of the section. The equation for the perimeter is P = 2(L + W). If the perimeter is 27 feet, solve for W. Show your work. (1 point)

27 = 2(L + W) 13.5 = (L + W) 35 = 3.5 x 10 3.5 + 10 = 13.5 W = 3.5

Part II: The equation for area is A = LW. Substitute the expression you found for W in Part I into the area equation. Then, if the area is equal to 35 square feet, write the equation in standard form with a, b, and c as whole numbers. (3 points)

L2 - 13.5L + 35 = 0

Part III: Use the quadratic formula, , to solve for L. Show your work. (2 points)

`\frac{-13.5 +or- \sqrt{13.5^(2)-4(35)(1) } }{2(1)}`

10 or 3.5

Part IV: Use the solution for L in Part III to find the corresponding values for W. Show your work. When you're done, state the dimensions of the section. (4 points)

L = 10 35 = LW 35 = 10 x 3.5 27 = 2(L + W) 27 = 2(10 + 3.5) 27 = 27

The length is 10 feet and the width is 3.5 feet.

Explanation:

Hope this helps

Answer 2

Perimeter
2l + 2w = 27
l + w = 13.5

Area
l*w = 35

(35 / l) + l = 13.5
35 + l^2 = 13.5l
l^2 - 13.5l + 35 = 0

Using this equation, we can find the length first
then width can be found