Answer:
47.6m.
Step by step solution:
Perimeter of a triangle = base + 2 . length____(1)
Area of a triangle = 1/2 . base . diagonal
108 = 1/2 . base . 15
multiplying both sides by 2:
216 = 15 . base
dividing both sides by 15:
base = 14.4m
But the diagonal divides the triangle into two
right angle triangles each with the same length (hypotenuse),base and diagonal(height).
Taking one right angle triangle:
And using pythagoras theorem;
length² = base² + diagonal ²
length² = 7.2² + 15²
Note: Base of each right angle triangle is 7.2 which would sum up to be 14.4 the base of the full triangle.
length² = 276.84
taking the square root of both sides:
length = 16.6m
Putting the values of the base and length into equation (1).
Perimeter of the triangle = 14.4 + 2 . 16.6
Note: We are dealing with the whole triangle
now hence the base is 14.4m.
Perimeter of the triangle = 14.4 + 33.2 = 47.6m.
Answer:
42m
Step-by-step explanation:
Let's call the rectangle ABCD. Since this is a rectangle, the triangles inside this rectangle (ΔACD and ΔABD) are both right triangles because of the definition of a rectangle. In addition, AB = CD and AC = BD because of the definition of a rectangle. Since AD = 15 (The Diagonal), you can say that because of Pythagorean Triples that AC = 9 and CD = 12 (3 : 4 : 5 = 9 : 12 : 15). Since we stated that AB = CD and AC = BD, we can say that the perimeter of ABCD is equal to 9 + 9 + 12 + 12. 9 + 9 + 12 + 12 is equal to 42.
Therefore: Perimeter of ABCD = 42
