Question

LMNO is a parallelogram. OP is perpendicular to LM. Given OM= 20 cm, LP= 9 cm and area of triangle LPO=54 square cm. Find the perimeter and area of parallelogram LMNO. ​

Answer 1

Answer

Area is base * height

18 * √319

18√319

Perimeter is sum of all sides

18+18+√72+√72

36+6√2+6√2

36+12√2

Answer 2

Area of parallelogram=225 square cm

Perimeter of parallelogram=80 m

Step-by-step explanation:

OM=20 cm

LP=9 cm

Area of triangle LPO=54 square cm

Area of triangle LPO=$\frac{1}{2}\times base\times height=\frac{1}{2}\times LP\times OP$

$\frac{1}{2}\times 9\times OP=54$

$OP=\frac{54\times 2}{9}=12 cm$

In triangle LPO

$OL^2=OP^2+LP^2$

Using Pythagoras theorem

$(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2$

$OL^2=(12)^2+9^2=144+81=225$

$OL=\sqrt{225}=15 cm$

In triangle OPM

$OM^2=PM^2+OP^2$

$(20)^2=PM^2+(12)^2$

$400=PM^2+144$

$PM^2=400-144=256$

$PM=\sqrt{256}=16 cm$

$LM=LP+PM=16+9=25 cm$

LM=ON=25 cm

OL=MN=15 cm

Area of parallelogram=$base\times height=25\times 9=225 cm^2$

Perimeter of parallelogram=$25(2)+15(2)=50+30=80 m$

#Learns more:

https://brainly.in/question/13596932:answered by Bijaymourya