Question

In a rectangular field PQRS of area 1200 m- side PQ divides into four equal parts by A. B and C. What is the ratio of area of PQRS and area of ABR​

Answer 1

Answer:

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Answer 2

Given:

a rectangular field with an area of 1200 m²

side PQ is divided by 4 parts by point A, B, C

To Find:

$\frac{ar(PQRS)}{ar(ABR)}$

Solution:

Let PQ= l and  QR= b

area of rectangle = length × breadth

                      1200  = l × b

as PQ divide into 4 equal part therefore AB = l/4

Area of Δ ABR = 1/2 × AB × QR         ( where PQ is the height of triangle)

                         = 1/2 × l/4 × b

                            =( l × b )/8

$\frac{ar(PQRS)}{ar(ABR)}$ =  ($\frac{ ( l b )}{( l b )/8}$

$\frac{ar(PQRS)}{ar(ABR)}$  = 8

Hence, the ratio is 8:1.