
![\textit{and their root difference is }4\frac{1}{3}\implies \cfrac{13}{3}\qquad so \\ \quad \\ \left[ \cfrac{-b+\sqrt{b^2-4(3)(10)}}{2(3)} \right]-\left[ \cfrac{-b-\sqrt{b^2-4(3)(10)}}{2(3)} \right]=\cfrac{13}{3} \\ \quad \\ \left[ \cfrac{-b+\sqrt{b^2-4(3)(10)}}{6} \right]+\left[ \cfrac{+b+\sqrt{b^2-4(3)(10)}}{6} \right]=\cfrac{13}{3} \\ \quad \\ \cfrac{-b+\sqrt{b^2-4(3)(10)}+b+\sqrt{b^2-4(3)(10)}}{6}=\cfrac{13}{3} \\ \quad \\ \cfrac{2\sqrt{b^2-4(3)(10)}}{6}=\cfrac{13}{3}](https://tex.z-dn.net/?f=%5Ctextit%7Band%20their%20root%20difference%20is%20%7D4%5Cfrac%7B1%7D%7B3%7D%5Cimplies%20%5Ccfrac%7B13%7D%7B3%7D%5Cqquad%20so%0A%5C%5C%20%5Cquad%20%5C%5C%0A%5Cleft%5B%20%5Ccfrac%7B-b%2B%5Csqrt%7Bb%5E2-4%283%29%2810%29%7D%7D%7B2%283%29%7D%20%5Cright%5D-%5Cleft%5B%20%5Ccfrac%7B-b-%5Csqrt%7Bb%5E2-4%283%29%2810%29%7D%7D%7B2%283%29%7D%20%5Cright%5D%3D%5Ccfrac%7B13%7D%7B3%7D%0A%5C%5C%20%5Cquad%20%5C%5C%0A%5Cleft%5B%20%5Ccfrac%7B-b%2B%5Csqrt%7Bb%5E2-4%283%29%2810%29%7D%7D%7B6%7D%20%5Cright%5D%2B%5Cleft%5B%20%5Ccfrac%7B%2Bb%2B%5Csqrt%7Bb%5E2-4%283%29%2810%29%7D%7D%7B6%7D%20%5Cright%5D%3D%5Ccfrac%7B13%7D%7B3%7D%0A%5C%5C%20%5Cquad%20%5C%5C%0A%5Ccfrac%7B-b%2B%5Csqrt%7Bb%5E2-4%283%29%2810%29%7D%2Bb%2B%5Csqrt%7Bb%5E2-4%283%29%2810%29%7D%7D%7B6%7D%3D%5Ccfrac%7B13%7D%7B3%7D%0A%5C%5C%20%5Cquad%20%5C%5C%0A%5Ccfrac%7B2%5Csqrt%7Bb%5E2-4%283%29%2810%29%7D%7D%7B6%7D%3D%5Ccfrac%7B13%7D%7B3%7D)
and I'm pretty sure you can take it from there
Ur answer in attachment hope it helps you
Answer:
The value of x is 8cm. The length of 3 sides are 8cm, 15cm and 17cm.
Step-by-step explanation:
Using Pythagoras' Theorem, a²+b² = c² :
Let a be x cm,
Let b be x+7 cm,
Let c be 2x+1 cm
x² + (x+7)² = (2x+1)²
x² + x² + 14x + 49 = 4x² + 4x + 1
2x² + 14x + 49 = 4x² + 4x + 1
Then, move all the variables to one side and solve it to find the value of x :
4x² + 4x + 1 - 2x² - 14x - 49 = 0
2x² - 10x - 48 = 0
2(x² - 5x - 24) = 0
x² - 5x - 24 = 0
(x-8)(x+3) = 0
x - 8 = 0
x = 8 cm
x + 3 = 0
x = -3 cm (rejected)
Substitute the x value into the length of a,b and c :
a = x
= 8 cm
b = x + 7
= 8 + 7
= 15 cm
c = 2x + 1
= 2(8) + 1
= 16 + 1
= 17 cm
B...................................
If fencing costs $5 per meter then the cost of fence to enclose the patio will be $ 120. Then the correct option is C.
<h3>What is a rectangle?</h3>
It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
Shelley plans to enclose the patio with fencing.
The dimension of the patio is 12 meters by 6 meters.
Then the perimeter of the patio will be
Perimeter = 2 (12 + 6) - 12
Perimeter = 2 x 18 - 12
Perimeter = 36 - 12
Perimeter = 24 meters
If fencing costs $5 per meter.
Then the cost fence to enclose the patio will be
Cost = 5 x 24
Cost = $ 120
More about the rectangle link is given below.
brainly.com/question/10046743
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