Sam is an apprentice carpenter whose boss asked him to construct a perfectly rectangular frame with a diagonal brace. When Sam had finished his boss measured the width of the frame to be 50 cm, the length to be 90 cm and the diagonal brace to be 100 cm. was Sam's boss happy with his work? Use mathematics to explain how you determined your answer

If it's a perfectly rectangle frame with W = 50 cm & L = 90 cm

So the right diagonal should be √ (50² + 90²) = √10600 = 102.96 cm

as per the calculation the diagonal should have a length of 102.96 cm, but the boss found 100 cm, that means their should be a frame which diagonal equal to 100 cm, short by 2.96 cm, that means short by 2.96/2 = 1.48 cm from the bottom & 1.48 cm from the top (same as well as for the 2nd diagonal)

In this case the boss should be happy