First slide

Cartesian plane

Question

OPQR is a square and M, I{ are the middle points of the sides PQ and QR, respectively, Then the ratio of the area of the square to that of triangle OMN is

Moderate

A

4:1
B

2:1
C

8:3
D

7:3

Solution

Let the coordinates of vertices O, P, Q,, R be (0, 0), (a, 0), (a, a), (0, a),respectively. Then, we get the coordinates of M as (a, a/2) and those of N as (a/2, a).
Therefore, Area of $ΔOMN = \frac{1}{2} |\begin{array}{ccc} 0 & 0 & 1 \\ a & a / 2 & 1 \\ a / 2 & a & 1 \end{array}| = \frac{3 a^{2}}{8}$
The area of the square is a².Hence, the required ratio is 8 : 3.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App