Question

Assertion: In the figure, AC = 17 cm, CD = 7 cm and AE = 15 cm, then ED = 15 cm.

Reason: BC = ED.

 

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given, AC = 17 cm, CD = 7 cm, AE = 15 cm

The figure includes several right angles rectangles and right triangles.

We are to assess this Assertion–Reason statement:

Assertion (A):

ED = 15 cm

Let’s verify it.

From the figure:

AE = AB + BE

AE = 15 cm

CD = 7 cm

In rectangle BCDE:

BC = ED   ...(Opposite sides of a rectangle are equal)

BE = CD = 7 cm

So, ED = AE – BE = 15 – 7 = 8   ...(Not 15)

The figure shows:

AE = AB + BE and BE = CD = 7 cm

So AB = AE – BE = 15 – 7 = 8 cm

BC is horizontal in rectangle.

So, ED = BC vertical rectangle; they are equal.

Therefore:

AB = 8 cm

From triangle ΔABC, with right angle at B:

`AC = sqrt(AB^2 + BC^2)`

⇒ 17² = AB² + BC²

⇒ 289 = 64 + BC²

⇒ BC² = 225

⇒ BC = 15

Since BC = ED, then ED = 15 cm

Reason (R):

In the figure, BCDE is a rectangle.

Therefore, opposite sides are equal.

BC = ED