Question

If the area of the blue square is 144 units2 and the area of the pink square is 1225 units2, then the length of the hypotenuse is:

Answer 1

Answer: 37 units

Explanation:

`Blue=144units^2` This also works as the height of the triangle.

`Pink=1225units^2` This also works as the base of the triangle.

Let's call pink ''a'', and blue ''b''. The side we're looking for ''c'' is the hypothenuse.

To find the values of a and b, use the area formula of a square and solve for a side. In this case, since we're going to need the squared values, this step can be omitted.

`Formula: A=s^2`

`s=\sqrt[]{A}`

Let's work with Blue.

`s=\sqrt[]{144units^2} \\s=12units`

Now Pink.

`s=\sqrt[]{1225units^2}\\s=35units`

So we have a triangle with a base of 35 units and a height of 12 units.

Now let's use the pythagoream's theorem to solve.

`c^2=a^2+b^2\\c=\sqrt[]{a^2+b^2} \\c=\sqrt[]{(12units)^2+(35units)^2}\\c=\sqrt[]{144units^2+1225units^2}\\ c=\sqrt[]{1369units^2}\\ c=37units`