Home
Class 14
MATHS
In DeltaABC,angleBAC=90^(@)andAD is dra...

In `DeltaABC,angleBAC=90^(@)andAD` is drawn perpendicular to BC . If BD -=7 cm and CD = 28 cm , what is the length (in cm ) of Ad ?

A

`3.5`

B

7

C

`10.5

D

14

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the length of AD in triangle ABC, where angle BAC is 90 degrees, and AD is drawn perpendicular to BC. Given that BD = 7 cm and CD = 28 cm, we can use the property of right triangles. ### Step-by-Step Solution: 1. **Identify the Triangle and Given Values**: - We have triangle ABC with a right angle at A. - We know that BD = 7 cm and CD = 28 cm. 2. **Use the Property of Right Triangles**: - In a right triangle, if a perpendicular is drawn from the right angle to the hypotenuse, the length of the perpendicular (AD) can be found using the formula: \[ AD^2 = BD \times CD \] - Here, BD is the length from B to D, and CD is the length from C to D. 3. **Substitute the Values**: - Substitute the known values into the formula: \[ AD^2 = 7 \times 28 \] 4. **Calculate the Product**: - Calculate the product: \[ AD^2 = 7 \times 28 = 196 \] 5. **Find the Length of AD**: - To find AD, take the square root of both sides: \[ AD = \sqrt{196} = 14 \text{ cm} \] ### Conclusion: The length of AD is 14 cm.
Promotional Banner

Similar Questions

Explore conceptually related problems

In a triangle ABC, angleBCA = 90^(@) and CD is perpendicular to AB. If AD = 4 cm and BD = 9 cm, then the value of DC will be

In a triangleABC, angleBCA = 90^@ and CD is perendicular to AB. If AD = 4 cm and BD = 9 cm, then the value of DC will be

In a triangle ABC , angle BAC= 90^@ and AD is perpendicular to BC where D is a point on BC. If BD = 4 cm and CD = 5cm then the length of AD is equal to: triangle ABC में, angle BAC= 90^@ और AD, BC पर लंबवत है जहाँ D, BC पर एक बिंदु है। यदि BD =4 सेमी और CD =5 सेमी तो AD की लंबाई ज्ञात करे

In DeltaABC,angleC=90^(@) and CD is perpendicular to AB at D. If (AD)/(BD)=sqrtk , then (AC)/(BC)=?

In a right angled DeltaABC, angleC=90^(@) and CD is the perpendicular on hypotenuse AB if BC = 15 cm and AC = 20 cm then CD is equal to :

In DeltaABC, /_A is right angle and AD is perpendicular to BC. If AD=4 cm, BC=12 cm, then value of (cotB+cotC)=

In the figure given below, ABC is a triangle with AB perpendicular to BC. Further BD is perpendicular to AC. If AD = 9 cm and DC = 4 cm, then what is the length of BD ?