a mailbox is 55 inches tall and casts a shadow that is 70 inches long. a nearby flagpole casts a shadow that is 196 inches long. how tall is the flagpole?

154 inches tall.

Step-by-step explanation:

In this scenario, the sun's angle is the same for both objects. Since we have three values and 1 variable (height of the pole) we can use the Rule of Three to solve this. In this, we simply multiply the diagonal values of the ratios and divide by the third value to get the value of the variable like so...

55 in.  <>  70 in.

x  <>  196 in.

(55 * 196) / 70 = x

10,780 / 70 = x

154 in. = x

Finally, we can see that the flagpole is 154 inches tall.

So,

Let l represent the length and w represent the width.

The first statement translates to:
2l + 2w = 72

The second statement translates to:
l = 2w

We will use substitution, as this is the easiest method.
2(2w) + 2w = 72

Distribute.
4w + 2w = 72

Collect Like Terms.
6w = 72

Divide both sides by 6.
w = 12

l = 2w
l = 2(12)
l = 24

Check.
2(24) + 2(12) = 72
48 + 24 = 72
72 = 72 This checks.

Length = 24 cm
Width = 12 cm