### The diagonal of a rectangle is thrice the length of its smaller side. What is the ratio of its length and breadth?

**Answer:**

2√2:1

**Step by Step Explanation:**

Let us assume that ABCD is a rectangle.- Let
**b**and**l**be the breadth(smaller side) and length of the rectangle, respectively.

Since, the diagonal of the rectangle is thrice the length of its smaller side.

Therefore, the length of the diagonal =**3b cm**. - On looking at the rectangle ABCD carefully, we notice that ABC is a right angled triangle where AB, BC, and AC are the breadth, length, and diagonal of the rectangle, respectively.

Now, in the right angled triangle ABC,

AC^{2}= AB^{2}+ BC^{2}

⇒ (3b)^{2}= b^{2}+ l^{2}

⇒ 9b^{2}- b^{2}= l^{2}

⇒ (9 - 1)b^{2}= l^{2}

⇒ 8b^{2}= l^{2}

⇒ l^{2}= 8b^{2}

⇒

=l ^{2}b ^{2}8 1

⇒ (

)l b ^{2}=8 1

⇒

=l b 2√2 1

⇒**l:b = 2√2:1** - Therefore, we can say that the ratio of the length and breadth of the rectangle is
**2√2:1.**