The diagonals of rectangle nopq intersect at point r. if qr=3x-4 and np=5x+20, solve for x.
2 answers:
Answer:
The value of "x" is 28.
Step-by-step explanation:
As can see in the attach the length of both diagonals is the same. From the problem, you have the length of segment qr = 3x -4, which represents half of the diagonal. Then, length of segment np = 5x + 20, is the completa diagonal. So, you have to multiply the equation for qr by 2 and then equal it to equation of segment np.
2·(3x - 4) = 5x + 20 ⇒ 6x - 8 = 5x + 20 ⇒ 6x - 5x = 20 + 8 ⇒ x = 28.
Summarizing the value of "x" is 28.
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Perimeter = 16.4 units
Using the heron's formula, Area ≈ 10.4 units².
<h3>What is the Heron's Formula?</h3>The heron's formula is used to find the area of a triangle with known side lengths of all its three sides, a, b, and c. The heron's formula is given as: Area = √[s(s - a)(s - b)(s - c)], where s = half the perimeter of the triangle
s = (a + b + c)/2.
Given the following:
K (-4,-1) ,
L(-2, 2),
M (3,-1)
Use the distance formula, d = , to find KL, LM, and KM.
KL = √[(−2−(−4))² + (2−(−1))²]
KL = √13 ≈ 3.6 units
LM = √[(−2−3)² + (2−(−1))²]
LM = √34 = 5.8 units
KM = √[(−4−3)² + (−1−(−1))²]
KM = √49 = 7 units
Perimeter = 3.6 + 5.8 + 7 = 16.4 units
Semi-perimeter (s) = 1/2(16.4) = 8.2 units
KL = a ≈ 3.6 units
LM = b = 5.8 units
KM = c = 7 units
s = 8.2
Plug in the values into √[s(s - a)(s - b)(s - c)]
Area = √[8.2(8.2 - 3.6)(8.2 - 5.8)(8.2 - 7)]
Area = √[8.2(4.6)(2.4)(1.2)]
Area = √108.6336
Area ≈ 10.4 units²
Learn more about heron's formula on:
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After graphing the lines, you can see that the solution is (4, -1)
