Question

Triangles ABC and CDE are mathmatecilly similar. work out the length of DE. WORK OUT THE LENGHT OF AB

Answer 1

`DE = 15`

`AB = 6`

Explanation:

Given

See attachment for triangles

Required

Determine the lengths of DE and AB

To solve for DE, we make use of the following equivalent ratio

`AC : BC =CE:DE`

Substitute values

`8:5 = 24:DE`

Express as fraction

`(8)/(5) = (24)/(DE)`

Cross Multiply

`DE * 8 = 24 *5`

`DE * 8 = 120`

`DE = 120/8`

`DE = 15`

To solve for AB, we make use of the following equivalent ratio

`AB : BC =CD:DE`

Substitute values

`AB : 5 = 18 : 15`

Express as fraction

`(AB)/(5) = (18)/(15)`

Multiply by 5

`5 * (AB)/(5) = (18)/(15)*5`

`AB= (18)/(15)*5`

`AB= (18)/(3)`

`AB = 6`