Answer:
(E) 25
Step-by-step explanation:
To find the area of triangle DBF, we need to determine the height DB, which is the same as DE since DE is perpendicular to BC and DE = DB.
First, we find the length of BH. Since FH is 13 cm and BF is 5 cm, BH is the difference between FH and BF:
BH = FH - BF = 13 cm - 5 cm = 8 cm
Now, we can use the Pythagorean theorem to find DB. Triangle DBH is a right triangle with DB as one leg and BH as the other leg:
DB^2 + BH^2 = DH^2
We know DH is the hypotenuse and its length is 13 cm:
DB^2 + 8^2 = 13^2
DB^2+64=169
DB^2 = 169-64
DB^2 = 105
DB= √105
DB~10.25 cm
Now we can calculate the area of triangle DBF using the formula for the area of a triangle:
Area = 1/2 x base × height
Substituting the base BF = 5 cm and height DB~10.25 cm:
Area~1/2×5×10.25
Area~1/2x 51.25
Area~25.625 cm^2
The area of triangle DBF is approximately 25.625 cm^2. Looking at the options provided, the closest answer is (E) 25.
