Question

Edwina measured the length of this swimming pool by drawing similar triangles as shown. What is the best estimate of p, the length of the swimming pool?

Answer 1

The measure of length of side p is 33 ft

Explanation:

Given as the length of the swimming pool measured by drawing similar triangle :

I.e The smaller Triangle similar to larger Triangle

Let o is the points of meeting of two triangles

And OAB is smaller triangle having sides OA , AB , BO

The measure of side OA = 8 ft

The measure of side AB = 12 ft

Again, OPQ is larger triangle having sides OP , PQ , QO

The measure of side OP = 22 ft

The measure of side PQ = p ft

∵ both Δ OAB and ΔOPQ are similar

The from similarity property

`(PQ)/(AB)` =
`(OP)/(OA)`

I.e
`(p)/(12)` =
`(22)/(8)`

Or,
`(p)/(12)` =
`(11)/(4)`

∴ p =
`(11)/(4)` × 12

or. p = 11 × 3

I.e p = 33 ft

Hence The measure of length of side p is 33 ft . Answer