Question

in the given figure ABCD is a square if AC + BD = 24 then AB is equals to ​

Answer 1

The length of AB is 6√2

Given,

• ABCD is a square
• AC + BD = 24

To Find,

The length of AB

Solution,

∵ ABCD is a square

∴ AB = BC = CD = AD (all sides of a square are equal)

Also,

∵ All the angles of a square are 90°

∴ ∠DAB = 90°

Now,

using Pythagoras Theorm in ΔABD, we get,

AB² + AD² = BD²
⇒ 2*AB² = BD²  (∵ AB = AD)

⇒ BD = AB√2

We know that,

Diagonals of a square are equal

∴ BD = AC

⇒ AC = AB√2

∵ AC + BD = 24 (Given)

⇒ AB√2 + AB√2 = 24

⇒ AB 2√2  =  24

⇒ AB  =  24 / (2√2)

⇒ AB = 6√2

Therefore, the length of AB is 6√2.

Answer 2

The length of AB is 6√2.

Given,

A figure in which ABCD is a square and the value of AC + BD is 24.

To Find,

The length of AB.

Solution,

Since it is given that ABCD is a square.

So, AB = BC = CD = AD (all sides of a square are equal)

Also,

All the angles of a square are 90°

∠DAB = 90°

Now,

Using Pythagoras Theorm in ΔABD,

AB² + AD² = BD²

2*AB² = BD²  (∵ AB = AD)

BD = AB√2

Also, the diagonals of a square are equal

So, BD = AC

AC = AB√2

AC + BD = 24 (Given)

AB√2 + AB√2 = 24

AB 2√2  =  24

AB  =  24 / (2√2)

AB = 6√2

Therefore, the length of AB is 6√2.

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