The perimeter of a rectangle is 152 inches. The ratio of the base to altitude of the rectangle is 6 to 13. Find the lengths of the base and the altitude

The perimeter of a rectangle is given by 2 (W+L) where L is the base and W is the altitude. If the ratio of W:L is

6: 13 then multiplying by a constant k

we get L = 13k and W=6k

therefore 2 (13k + 6k) = 152 inches

2 (19k) = 152

38k = 152

k = 4

Thus since the altitude is equal to 13k then it is equivalent to 52.

Therefore the length of the altitude is 52 inches

First, let x be the common factor between the lengths of the base and the altitude of the given rectangle such that these can be expressed as 6x and 13x, respectively. The perimeter of the rectangle is calculated through the equation,

P = 2B + 2A

where P is perimeter, B is base, and A is altitude. Substituting the given expressions,

152 = (2) 6x + (2) 13x

The value of x from the equation is 4. The lengths of the bases and the altitude are shown below.

base = 6 (4) = 24 inches

altitude = 13 (4) = 52 inches