Question

The perimeter of a rectangle is 104 centimeters the length of the rectangle is twelve more than the width find the dimensions of the rectangle

in detailed and organized steps

Answer 1

length = 32cm; width = 20cm

Explanation:

The answer to the question above is provided thus.

Formula for calculating the perimeter of a rectangle = 2(l + w)

Where,

l = length

w = width

Recall that perimeter is 104 cm and length is 12cm longer than the width.

Thus,

P = 2(l + w)

Since perimeter is 2 times l + w, we divide through by 2 to get l + w. That is:

`104cm = 2(l + w)`

Dividing through by 2

`(104cm)/(2) = (2(l + w))/(2)`

`52cm = l + w`

since length is length is 12cm longer than the width, we think of two numbers whose sum equals 52 and difference equals 12. The numbers are 32 and 20. That is, 32 + 20 = 52; 32 - 20 = 12.

Therefore,

104cm = 2( 32cm + 20cm)

Hence, length is 32cm while width is 20cm. The length is 12cm longer than the width such that 32cm - 20cm = 12cm.

Thus, the dimension of the rectangle whose perimeter is 104cm is 32cm + 20 cm or 32cm and 20cm.

Check,

Perimeter of a rectangle = 2( l + w)

104cm = 2( 32cm + 20cm)

104cm = 2(52cm)

104cm = 2 × 52cm

104cm = 104cm

Length is 12cm longer than the width

32cm - 20cm = 12cm