The perimeter of a rectangle is 108cm. The ration of its length to its width is 7:2 what is the area of the rectangle in cm2?

504 cm²

Step-by-step explanation:

Let the length and the width of the rectangle be L cm and W cm respectively.

Perimeter= 2(L +W)

2(L +W)= 108

L +W= 108 ÷2

L +W= 54

L= 54 -W -----(1)

Cross multiply:

2L= 7W -----(2)

Substitute (1) into (2):

2(54 -W)= 7W

Expand:

108 -2W= 7W

+2W on both sides:

9W= 108

Divide both sides by 9:

W= 108 ÷9

W= 12

Substitute W= 12 into (1):

L= 54 -12

L= 42

Area of rectangle

= length ×width

= LW

= 42(12)

= 504 cm²

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b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b