Question

I need the answer for my homework please help!

Answer 1

The values are
`\(x = (125)/(21)\)` and
`\(y = (25)/(3)\)`.

Let the triangle be ABC. In triangle ABC, where DE is drawn horizontally parallel to BC, we can use similar triangles to find the values of x and y. Since DE is parallel to BC, triangles ADE and ABC are similar.

The ratio of corresponding sides of similar triangles is equal. Therefore:

`\[ (AD)/(AB) = (DE)/(BC) \]`

Given that
`\(AD = 5\)`,
`\(AE = 7\)`, and
`\(BC = 10\)`, we can write:

`\[ (5)/(AB) = (7)/(10) \]`

Now, solve for AB:

`\[ AB = (5 * 10)/(7) = (50)/(7) \]`

Now, since DE and BC are parallel, the corresponding sides of the triangles are in proportion. Therefore:

`\[ (AD)/(AE) = (DC)/(EB) \]`

Plugging in the values:

`\[ (5)/(7) = (x)/(y) \]`

Now, solve for x and y:

`\[ x = (5y)/(7) \]`

Now, we know
`\(x = (5y)/(7)\)` and
`\(AB = (50)/(7)\)`. Since AB is the sum of x and y, we can write:

`\[ (50)/(7) = (5y)/(7) + y \]`

Now, solve for y:

`\[ (50)/(7) = (6y)/(7) \]`

`\[ 50 = 6y \]`

`\[ y = (25)/(3) \]`

Now that we have the value of y, we can find x:

`\[ x = (5y)/(7) = (5 * (25)/(3))/(7) = (125)/(21) \]`

So, the values are
`\(x = (125)/(21)\)` and
`\(y = (25)/(3)\)`.