One side of a rectangle is 6 meters shorter than four times another side. Find the length of the longer side if we also know tha

Question

tatiyna

2 years ago

8

One side of a rectangle is 6 meters shorter than four times another side. Find the length of the longer side if we also know tha

t the perimeter of the rectangle is 58 meters

Mathematics

2 answers:

Wittaler [7] · Answer 1 · 2023-05-02T18:45:56+03:00

Wittaler [7]2 years ago

6 0

Set the shorter side of rectangle as X m
The longer side = (4X-6) m
58 = (X + 4X -6)2
58=10X -12
70 = 10X
X = 7
The shorter side is 7 m
And the longer side is 4 x 7 -6 = 22 m

Lerok [7] · Answer 2 · 2023-05-02T21:01:30+03:00

Answer:

22 meters

Step-by-step explanation:

Let x = width of the rectangle

Let y = length of the rectangle

Equation 1

If the length of the rectangle is 6 meters shorter than four times the width then:

⇒ y = 4x - 6

Equation 2

Perimeter of a rectangle = 2(width + length)

If the perimeter is 58 inches, then:

⇒ 58 = 2(x + y)

Solve by substitution

Substitute Equation 1 into Equation 2 and solve for x:

⇒ 58 = 2(x + 4x - 6)

⇒ 58 = 2(5x - 6)

⇒ 58 = 2 · 5x - 2 · 6

⇒ 58 = 10x - 12

⇒ 58 + 12 = 10x -12 + 12

⇒ 10x = 70

⇒ 10x ÷ 10 = 70 ÷ 10

⇒ x = 7

Substitute found value of x into Equation 1 and solve for y:

⇒ y = 4(7) - 6

⇒ y = 28 - 6

⇒ y = 22

Conclusion

The dimensions of the rectangle are:

width = 7 meters
length = 22 meters

Therefore, the length of the longer side is 22 meters