Question

The area of a quadrilateral field is 1250 m². The measure of one of its diagonals is 50 m and the
measures of two perpendiculars on this diagonal are in the ratio 2:3. Find the measure of each
perpendicular.
​

Answer 1

$\boxed{\huge\mathbb{GIVEN-:}}$

$\implies area \:of \:quadrilateral \:field =1250m^2$

$\implies$one of its diagonal is 50m.

$\implies$ measure of two perpendicular diagonal are in ratio 2:3.

TO FIND-:

■MEASURE OF EACH PERPENDICULAR.

FORMULA:-

$\boxed { \green {area \: of \: quadrilateral = \frac{1}{2} \times d \times (h1 +h2)}}$

☆SOLUTION-:

$1250 = \frac{1}{2} \times 50 \times (2x + 3x) \\ \\ 1250 = \cancel{ \frac{50}{2} }(5x) \\ 25 \times 5x = 1250 \\ 125x = 1250 \\ x = \cancel \frac{1250}{125} \\ \boxed{ \green {\therefore \: x = 10}.}$

NOW-:

☆length of perpendiculars,

$2x = 2 \times 10 \implies20m. \\ 3x = 3 \times 10\implies30m.$