Question

ABCD is a quadrilateral with BC parallel to AD. CD is perpendicular to BC. BC=5cm and AD=12cm. The area of triangle BCD is 20cm². Find CD.

Answer 1

To find the length CD of the height of triangle BCD, we can use the formula for the area of a triangle and solve for CD.

Step-by-step explanation:

Let's solve this problem step by step:

1. Since BC is parallel to AD and CD is perpendicular to BC, we can see that triangle BCD is a right triangle.
2. We know the area of triangle BCD is 20cm², and the base BC is 5cm. So we can find the height CD using the formula for the area of a triangle: area = (base * height) / 2.
3. Plugging in the values we know, we get 20 = (5 * CD) / 2. Solving for CD, we find that CD = 8cm.