Un patrat si un dreptunghi au perimetre egale . Daca aria patratului este 81 cm patrati si lungimea dreptunghiuli este de 4 ori mai mare decat latimea acestuia , atunci aria dreptunghiului este egala cu :

the question in English

One square and one rectangle have equal perimeters. If the area of ​​the square is 81 cm square and the length of the rectangle is 4 times the width of the rectangle, then the rectangle area is equal to:

Let 
x--------> the length of the rectangle
y-------> the width of the rectangle

we know that
area of square=b²
where
b is the length side of square
area square=81 cm²
b²=81----------> b=9 cm

perimeter square=4*b-----> 4*9=36 cm

perimeter of rectangle=36 cm
perimeter of rectangle=2x+2y
so
2x+2y=36-----> equation 1
x=4y------> equation 2

substitute equation 2 in equation 1
2*[4y]+2y=36-----> 8y+2y=36-----> 10y=36-----> y=3.6 cm
x=4y-----> x=4*3.6------> x=14.4 cm

area rectangle=x*y------> 3.6*14.4-----> 51.84 cm²

the answer is 
the area of rectangle is 51.84 cm²

the answer in Romanian


lăsa
x-------->lungimea dreptunghiului
y-------> lățimea dreptunghiului

noi stim aia
zona de pătrat=b²
Unde
b -----> este lungimea laturii pătrate
zona de pătrat=81 cm²
b²=81----------> b=9 cm

pătrat perimetral=4*b-----> 4*9=36 cm

perimetrul dreptunghiului=36 cm
perimetrul dreptunghiului=2x+2y
asa de
2x+2y=36-----> ecuația 1
x=4y------> ecuația 2

substituția 2 din ecuația 1
2*[4y]+2y=36-----> 8y+2y=36-----> 10y=36-----> y=3.6 cm
x=4y-----> x=4*3.6------> x=14.4 cm

zona dreptunghiulară=x*y------> 3.6*14.4-----> 51.84 cm²

raspunsul este
aria dreptunghiului este de 51,84 cm²