Question

The length of a lacrosse field is 15 yards less than twice the width, and the perimeter in 270 yards. The defensive area of the field is 3/25 of the total field area. Find the defensive area of the lacrosse field.

Answer 1

The defensive area is 510 square yards

Step-by-step explanation:

Let L be the length of the rectangle

and

W be the width

According to given statement

L = 2W-15

Perimeter = 270

$P = 2W+2L\\270 = 2W + 2(2W-15)\\270 = 2W + 4W -30\\270 +30 = 6W\\6W = 300$

Dividing both sides by 6

$\frac{6W}{6} =\frac{300}{6}\\W = 50\ yards\\\\and\\L = 2(50) -15\\= 100-15\\=85\ yards$

We have to find the area first to find the defensive area

So,

$Area = L* W\\= 85 * 50\\=4250\ square\ yards$

Defensive area = 3/25 of total area

So,

$=\frac{3}{25}*4250\\=3 *170\\=510\ square\ yards$

Hence,

The defensive area is 510 square yards

Keywords: Area, Rectangle

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