Answer:
(d) 18 cm
Step-by-step explanation:
To find the length of BD, we can use the formula for the area of a quadrilateral:
Area = (1/2) * BD * (perpendicular1 + perpendicular2)
Given that the area of quadrilateral ABCD is 20 cm² and the perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm, we can substitute these values into the formula:
20 = (1/2) * BD * (1 + 1.5)
Next, we simplify the equation:
20 = (1/2) * BD * 2.5
To isolate BD, we divide both sides of the equation by 2.5:
120 / 2.5 = BD
18 = BD
Therefore, the length of BD is 18 cm.
So, the correct answer is (d) 18 cm.
To find the length of the diagonal BD, the formula for the area of a quadrilateral can be used. By applying this formula and solving for the length of BD, we find that it is 4 cm.
To find the length of the diagonal BD, we can use the formula for the area of a quadrilateral which is equal to the product of the perpendiculars on any side from the opposite vertices.
Let the length of the perpendicular from A be 1 cm and the length of the perpendicular from C be 1.5 cm. Let the length of BD be 'x'.
Then, the area of the quadrilateral ABCD is equal to the sum of the areas of triangles OAB, BCD, and EFG. Therefore, we have:
8 + 3 + 1 = 20
From this equation, we can solve for x and we get:
x = 4 cm
Therefore, the length of BD is 4 cm. The answer is (a) 4 cm.
