Same pattern as Rectangle ACEG — the shaded triangles. New numbers, new story. Try each one on paper, then check the working below — or watch it drawn out, the same way the problem above is.
Question 1
A rectangular garden PQRS is divided into two rectangular beds by a straight path UV, where U is on PQ and V is on SR (so PUVS and UQRV are the two beds). H is a sprinkler point on PS, D is a sprinkler point on QR, and M is the midpoint of UV. The perimeter of PQRS is 84 m and PS : PQ = 3 : 4. Find (a) PS, and (b) the total area of the shaded triangles HMV and UMD.
Work it out on paper, then check below. ▶ See the working
Question 2
A rectangular library hall JKLM is divided into two reading rooms by a glass partition NO, where N is on JK and O is on ML (so JNOM and NKLO are the two rooms). E is a bookshelf on JM, F is a bookshelf on KL, and W is the midpoint of NO. The perimeter of JKLM is 88 m and JM : JK = 5 : 6. Find (a) JM, and (b) the total area of the shaded triangles EWO and NWF.
Work it out on paper, then check below. ▶ See the working