TheCATExam
Sign in

CAT 1997 — QA Question 36

Basics of QuadrilateralsEasy
Passage / Data

Direction: Answer the questions based on the following information.

For these questions the following functions have been defined.

la(x, y, z) = min(x + y, y + z)

le(x, y, z) = max (x − y, y − z)

ma(x, y, z) = 12 [le(x, y, z) + la(x, y, z)]

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

Answer & solution

  • A

    √3 : 2

  • B

    1 : √3

  • C

    2 : 5

  • 3 : 4

Solution

Let L and B denote the length and the breadth of the rectangle. So the diagonal will be (L2+B2). Hence, from the condition given, (L + B) – (L2+B2)=12L

⇒(L2+B2)=L2+B

Squaring both sides, we get

(L2+ B2) = (L2+B)2

⇒ L2 = L24+LB

⇒ 3L24=LB

⇒ BL=34

Shortcut:
First write the relation (L + B) – (L2+B2)=12L.

or L2+B=(L2+B2)

Put the values of options. Option (d) satisfies. So the answer is (d).

CAT 1997 QA Q36: In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of th — Solution | TheCATExam