the figure shows a rectangle with its length and breath as indicated . given that the perimeter of the rectangle is 120 cm, find the area of the rectangle.?
Answers
Answer:
since opposite sides are equal
3x-y=2x+y
x=2y
y=x/2 ....(i)
thus new length=2x+y
=2x+(x/2) [using (i)]
=(4x+x)/2
l=5x/2 .....(ii)
now,
perimeter=2(l+b)=120cm
l+b=60cm
from figure and using (ii)
[5x/2]+2x-3=60
[5x+4x-6]/2=60
9x-6=120
9x=126
x=126/9
x=14 ..........(iii)
substitute (iii) in (i)
y=14/2
y=7 ...........(iv)
From figure,
length=2x+y [using (iii) and (iv)]
=2x14+7
length=35cm
breadth=2x-3
=2x14-3 ....[using(iii)]
=28-3
breadth=25cm
now,
Area=lxb
=35x25
=875cm^2
Answer:
area is 875 cm^2
Step-by-step explanation:
1st area of rectangle=l*b..,(i=length n b=breadth)
and perimeter of rectangle=sum of all sides..,
property of rectangle is that the opp. sides r always equal in length., and all angles will be 90 degrees..,
hence..,(3x-y)=(2x+y)
=>x=2y
and given that..,
120=2*(2*2y-3)+2(2*2y+y)
i.e 120=8y-6+8y+2y
i.e 126=18y
=> y=7 and x=14...
therefore area of rectangle=l*b
i.e a=35*25
=> a=875 cm^2