Question

A carpenter has a rectangular wooden board. The diagonal of the board is 18 inches long and one side of the board is 12 inches long
What was the perimeter of the rectangular board?



Enter your answer, rounded to the nearest hundredth, in the box.


____ in.

Answer 1

I’m pretty sure it’s 50.83 in

Answer 2

In this question, it is given that the diagonal of the board is 18 inches long and one side of the board is 12 inches long.

Let the other side is of length b inches .

Now we use pythagorean identity, which is

$a^2 + b ^2 = c^2$

Here, a = 12 and c=18

Substituting these values, we will get

$12^2 + b^2 = 18^2 \\ 144 + b ^2 = 324 \\ b^2 = 324-144 \\ b^2 = 180 \\ b= \sqrt{180} \\ b = 13.4164 inches$

And the formula of perimeter is

$Perimeter = 2(Sum\ of \ legs)$

Substituting the values of the two legs, we will get

$Perimeter = 2(12+13.4164) = 50.83 inches$