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23) A backyard has a perimeter of 144m.
a) If the backyard is square, what are the dimensions?
b) If the backyard is rectangular, and the length is three times the width, what are the dimensions?

Answer :

a) 144/4 = 36 metres per side
b) 18*3 = 54
54+54+18+18= 144 metres

dimensions would be 54 by 18

a. Side of square backyard = 36m and area = 1296m²

b. length and width of the rectangle backyard is 54m and 18m. Area =972m²

What is Perimeter ?

Perimeter is the sum of all the sides of a given 2D figure.

Perimeter of the backyard is given in this question which is 144m

a. In case of a square

We know that perimeter of a square is = 4×side

∴ 144 = 4×side

   side = 144/4

   side = 36m

Area of a square = (side)²

                           = (36)²

                           = 1296m²

b. In Case of a rectangle

We know that the perimeter of rectangle = 2(length + width)

given width = x and length = 3x

∴ 144 = 2(x + 3x)

  144 = 2(4x)

   144 = 8x

    x = 144/8

    x = 18m

So. the width of the rectangle = 18m

∴ the length is = 18×3 = 54m

Area of the rectangle = length × width

                                    = 18 × 54 = 972m²

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