Question

Please help

number 4 is in the picture I attached



and number 8 I typed out

the ratio of the length to the width of a rectangle is 4:11. The rectangle's perimeter is 650 mm. What are the rectangles dimensions? ​

Answer 1

4

If two triangles are similar, corresponding sides are in proportion. So, we have

`(17.5)/(14) = (2y)/(y+3)`

Multiply both sides by
`14(y+3)` to get

`17.5(y+3) = 28y`

Expand the left hand side:

`17.5y + 52.5 = 28y`

Subtract 17.5y from both sides:

`52.5 = 10.5y`

Divide both sides by 10.5:

`y = 5`

8

Given the ratio

`(x)/(y) = (4)/(11)`

we can deduce

`x = (4)/(11)y`

The perimeter of the rectangle is given by

`2x+2y = 2\cdot (4)/(11)y + 2y = (30)/(11)y = 650 \iff y = (715)/(3)`

Now we can deduce the value for x:

`x = (4)/(11)\cdot(715)/(3) = (260)/(3)`