Question 10. Five squares and two right triangles are arranged as shown. The numbers 3, 8, and 22 inside three of the squares indicate their areas in square meters. What is the area of the square containing the question mark? Take a closer look at the squares and triangles. Now, to find the area of a square, we do one side times another side. And since it is a square, we can just take one side squared. And if we have the area, we can find the length of a side by taking the square root of the area. Knowing this, we can try to figure out these triangles. So this one side will be the square root of 22. The other leg of the triangle is the square root of 3. And we know that these are right triangles. And the area for a right triangle is a squared plus b squared equals c squared. And we know that a squared and b squared are root 22 and root 3. So we input these into the formula, and this simplifies into 22 plus 3 equals c squared, or 25 equals c squared. So we know that the hypotenuse of this triangle will be 5. We now know the side of this square. And with this, we know that the other side is equal, since it is a square. So now we know the hypotenuse and one of the legs of the other triangle. All we need to do is find the leg of the other triangle. To do this, we again do a squared plus b squared equals c squared. This time, inputting root 8 into a and 5 into c. Simplifying, we get 8 plus b squared equals 25. This gives us b squared equals 17. So with this, we know that the area of the square with the question mark is going to be d, 17 meters squared.

area calculation

square properties

right triangles

hypotenuse

geometry problem