Question

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Answer 1

S O L U T I O N:-

Given:-

➡ AC = 10cm.

➡ DC = 9cm.

➡ AD = 17cm.

➡ AB ⊥ BC ➡ ∠ABD = 90°

To find:-

➡ Length of BC and AB.

Answer:-

➡ Length of BC is 6cm and length of AB is 8cm.

Step By Step Solution:-

By pythagoras theorem,

Hypotenuse² = Perpendicular² + Base²

Here,

∠B = 90°

So,

➡ x² + y² = AC²

Putting the value of AC here,

➡ x² + y² = 10

➡ x² + y² = 100 ......(i)

Also,

➡ AD² = AB² + BD²

➡ AD² = y² + (DC + x)²

Putting the values of AD and DC, we get,

➡ 17² = y² + (9 + x)²

➡ 289 = y² + (9² + 2×9×x + x²)

➡ 289 = y² + 81 + x² + 18x

From equation (i), y² = 100 - x²

So,

➡ 289 = 100 - x² + 81 + x² + 18x

➡ 289 - 100 - 81 = 18x

➡ 18x = 108

Dividing both sides by 18, we get,

➡ x = 6cm (Remember this)

Substituting the value of x in equation (i), we get,

➡ 6² + y² = 100

➡ y² = 100 - 36

➡ y² = 64

➡ y = √64

➡ y = ±8cm

Since, length cannot be negative, we omit y = -8cm.

So,

y = 8cm.

Hence,

➡ Length of BC = x = 6cm.

➡ Length of AB = y = 8cm.

Concept Used:-

➡ Pythagoras Theorem.

Answer 2

Answer:

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