The diagonal of a rectangle is thrice the length of its smaller side. What is the ratio of its length and breadth?
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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,
AC2 = AB2 + BC2
⇒ (3b)2 = b2 + l2
⇒ 9b2 - b2 = l2
⇒ (9 - 1)b2 = l2
⇒ 8b2 = l2
⇒ l2 = 8b2
⇒ =
⇒ ( )2 =
⇒ =
⇒ l:b = 2√2:1 - Therefore, we can say that the ratio of the length and breadth of the rectangle is 2√2:1.