Question

△ABC ~ △ADE. Find x.

Answer 1

Similar triangles states that if a triangles are similar then their corresponding ratios are in proportion.

As per the given statement:

`\triangle ABC \sim \triangle ADE`

Since, these two triangles ABC and ADE are Similar then:

Corresponding sides are in proportion: i,e

`(AC)/(AE) =(BC)/(DE)`

from the figure:

AC = x-1 units, AE = AC+CE = x-1+27 = x+26 units , BC = 20 units and DE = 3x+8 units

Substitute these values we get;

`(x-1)/(x+26) =(20)/(3x+8)`

By cross multiply we get;

`(x-1)(3x+8) = 20(x+26)`

The distributive property says that:

`a \cdot (b+c) = a\cdot b+ a\cdot c`

Using distributive property:

`3x^2+8x-3x-8 = 20x +520`

Combine like terms;

`3x^2+5x-8 = 20x +520`

or

`3x^2+5x-8-20x-520=0`

Combine like terms;

`3x^2-15x-528=0`

or

`3(x^2-5x-176)=0`

`x^2-5x-176=0`

Factorize the equation:

`x^2-16x+11x-176=0`

`x(x-16)+11(x-16)=0`

`(x-16)(x+11)=0`

By zero product property we have;

x-16 = 0 and x+ 11 = 0

x = 16 and x = -1

Since, side cannot be in negative

Therefore, the value of x = 16 units