A new Community sports complex is being built in Erie. The perimeter of the rectangular playing is 292 yards. The length of the field is 7 yards less than double the width. What are the dimensions of the playing field?

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 292 yards

The statement

The length of the field is 7 yards less than double the width is written as

l = 2w - 7

Substitute the expression into the above formula and solve for the width

292 = 2( 2w - 7) + 2w

292 = 4w - 14 + 2w

292 = 6w - 14

6w = 292 + 14

6w = 306

Divide both sides by 6

w = 51

Substitute this value into l = 2w - 7

That's

l = 2(51) - 7

l = 102 - 7

l = 95

Therefore we have

length = 95 yards

width = 51 yards

Hope this helps you

As we know two triangles are similar by the following Postulates:

1. Side-Side-Side Proportionality

2.Side-Angle-Side Proportionality

3.Angle - Angle Similarity

Given: Triangle MNO is dilated to create triangle PQR on a coordinate grid.

∠N ≅ ∠Q

As to prove similarity of two triangles , line segments that is corresponding sides of triangles can't be congruent.They must be proportional.

As well as we have to select angles in such a way As :ΔMNO~ΔPQR

⇒∠N→∠Q, ∠M→∠P, ∠O→∠R

The option : Angle M is congruent to angle P is true.