Question

PLEASE HELP ALL INFO IN THE IMAGE PLS ANSWER ASAP

Answer 1

Let's see

• 13/x+2=(x+13)/x+17
• 13x+221=13x+26+x²+2x
• x²+2x-195=0
• (x+15)(x-13)=0
• x=-15,13

Length must be positive so x=13

Answer 2

x = 13

Explanation:

In similar triangles, corresponding sides are always in the same ratio.

Therefore the ratio of the left side of the largest triangle to its base is equal to the ratio of the left side of the smallest triangle to its base.

`\implies 13:(x+2)=(13+x):(x+17)`

Solve for x:

`\implies (13)/(x+2)=(13+x)/(x+17)`

`\implies 13(x+17)=(13+x)(x+2)`

`\implies 13x+221=13x+26+x^2+2x`

`\implies x^2+2x-195=0`

`\implies x^2+15x-13x-195=0`

`\implies x(x+15)-13(x+15)=0`

`\implies (x-13)(x+15)=0`

`\implies x=13`

`\implies x=-15`

As length is positive, x = 13 only.