In rectangle ABCD, side AD = 12m, side CD is 3m shorter, and diagonal BD is the same length than AD.

In rectangle ABCD, side AD = 12m, side CD is 3m shorter, and diagonal BD is the same length than AD. Find the perimeter and areas of rectangle ABCD and triangle ABD.

The length of the rectangle is known by condition, we find the width and diagonal:
CD = AD – 3 = 12 – 3 = 9 m – width;
BD = AD + 3 = 12 + 3 = 15 m – diagonal.
Knowing the sides, we find:
1. Perimeter and area of rectangle ABCD:
P = 2 * (a + b) = 2 * (AD + CD) = 2 * (12 + 9) = 2 * 21 = 42 m.
S = a * b = AD * CD = 12 * 9 = 108 m².
2. Perimeter and area of triangle ABD:
P = a + b + c = 12 + 9 + 15 = 36 m.
S = 1/2 * a * h = 1/2 * 12 * 9 = 54 m².
Answer: rectangle ABCD: P = 42 m, S = 108 m², triangle ABD: P = 36 m, S = 54 m².