Answer:
Step-by-step explanation:
Let the sides of the triangle be a, b and c.
<u>We have:</u>
- P = a + b + c = 29
- a = 2b - 5
- c = b + 6
<u>Substitute values and solve for b:</u>
- 2b - 5 + b + b + 6 = 29
- 4b + 1 = 29
- 4b = 28
- b = 7
<u>Find a and c:</u>
- a = 2*7 - 5 = 14 - 5 = 9
- c = 7 + 6 = 13
<u>The sides are:</u> 7, 9, 13
Given :
- The length of a rectangle is 4m more than the width.
- The area of the rectangle is 45m²
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To Find :
- The length and width of the rectangle.
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Solution :
We know that,
![\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\:](https://tex.z-dn.net/?f=%5Cqquad%20%7B%20%5Cpmb%7B%20%5Cbf%7BLength%20%5Ctimes%20Width%20%3D%20Area_%7B%28rectangle%29%7D%7D%7D%7D%5C%3A)
So,
Let's assume the length of the rectangle as x and the width will be (x – 4).
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Now, Substituting the given values in the formula :
![\qquad \sf \: { \dashrightarrow x \times (x - 4) = 45 }](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5C%3A%20%7B%20%5Cdashrightarrow%20x%20%20%5Ctimes%20%20%28x%20-%204%29%20%3D%2045%20%7D)
![\qquad \sf \: { \dashrightarrow {x}^{2} - 4x = 45 }](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5C%3A%20%7B%20%5Cdashrightarrow%20%7Bx%7D%5E%7B2%7D%20%20-%204x%20%3D%2045%20%7D)
![\qquad \sf \: { \dashrightarrow {x}^{2} - 4x - 45 = 0 }](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5C%3A%20%7B%20%5Cdashrightarrow%20%7Bx%7D%5E%7B2%7D%20%20-%204x%20-%2045%20%3D%200%20%7D)
![\qquad \sf \: { \dashrightarrow {x}^{2} - 9x+ 5 x - 45 = 0 }](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5C%3A%20%7B%20%5Cdashrightarrow%20%7Bx%7D%5E%7B2%7D%20%20%20%20-%209x%2B%205%20x%20-%2045%20%3D%200%20%7D)
![\qquad \sf \: { \dashrightarrow x(x - 9) + 5(x - 9) = 0 }](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5C%3A%20%7B%20%5Cdashrightarrow%20x%28x%20-%209%29%20%2B%205%28x%20-%209%29%20%3D%200%20%7D)
![\qquad \sf \: { \dashrightarrow (x - 9) (x + 5) = 0 }](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5C%3A%20%7B%20%5Cdashrightarrow%20%28x%20%20-%209%29%20%28x%20%20%2B%205%29%20%3D%200%20%7D)
![\qquad \sf \: { \dashrightarrow x = 9, \: \: x = - 5}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%5C%3A%20%7B%20%5Cdashrightarrow%20x%20%3D%209%2C%20%5C%3A%20%5C%3A%20x%20%3D%20%20-%205%7D)
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Since, The length can't be negative, so the length will be 9 which is positive.
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![\qquad { \pmb{ \bf{ Length _{(rectangle)} = 9\:m}}}\:](https://tex.z-dn.net/?f=%5Cqquad%20%7B%20%5Cpmb%7B%20%5Cbf%7B%20Length%20_%7B%28rectangle%29%7D%20%3D%209%5C%3Am%7D%7D%7D%5C%3A)
![\qquad { \pmb{ \bf{ Width _{(rectangle)} = 9 - 4=5\: m}}}\:](https://tex.z-dn.net/?f=%5Cqquad%20%7B%20%5Cpmb%7B%20%5Cbf%7B%20Width%20_%7B%28rectangle%29%7D%20%3D%209%20-%204%3D5%5C%3A%20m%7D%7D%7D%5C%3A)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
It's C because 1 and 5 are the same angles so they are parallel.
Answer:
-32r-12
Step-by-step explanation:
Solve by distributing the -4 (multiplying -4 by the numbers in parentheses)
There is the equal values method, so you can do:
x-4 = 4x-10 (remove x from both sides)
-4 = 3x -10 (add ten to both sides)
6 = 3x (devide by 3x)
2 = x
Check: (by plugging it into the equation)
y = 2-4 and y = 8-10
y = -2 and y = -2
that's matches so it is correct...
YOUR ANSWER IS:
(2, -2)
I hoped I helped sort things out, and have a great day!