Question

Hi can someone help me with math homework

Answer 1

Shorter section is (mm):
159

Longer section is (mm):
211

Explanation:

Let x represent the longer section length and y the shorter section length

We are given x : y = 4:3

We can rewrite in fractional form as

`(x)/(y) = (4)/(3)`

Multiply both sides by y to get

`(x)/(y) \cdot y = (4)/(3)y\\\\x = (4)/(3)y`

We know that the combined length of both sections is 370 mm
x + y = 370

Substitute the expression for x in the above equation

`(4)/(3)y + y = 370\\\\(4)/(3)y + y = y((4)/(3) + 1})\\= y((4)/(3) + (3)/(3))\\\\= y((7)/(3))\\\\= (7)/(3)y`

Therefore we get

`(7)/(3) y= 370\\\\`

Multiply both sides by
`(3)/(7)`

`(7)/(3) y * (3)/(7) = 370 * (3)/(7) \\\\y = 158.57\; mm\\`

= 159 mm (to 3 significant figures)

Therefore the longer section = 370 - 159 = 211 mm

Check the ratio to verify

211/159 = 1.327 ≈ 1.33 which is 4/3