5. The breadth of a rectangle is 8 cm less than its length. Ifdhe length is increased by 4 cm and breadth is increased by
9 cm, the area of the rectangle is found to increase by 147 sq cm. Find the length and breadth of the rectangle.
Answers
Step-by-step explanation:
We have,
Let the length of rectangular board=xcm.
The breadth =ycm.
Now,
According to given question,
length=breadth+8
x=y+8......(1)
Again, according to given question,
(x−4)2y=256
⇒(x−4)y=128
⇒xy−4y=128......(2)
Put the value of x in equation ( 2) and we get,
(y+8)y−4y=128
⇒y
2
+8y−4y−128=0
⇒y
2
+4y−128=0
Using quadratic formula and we get,
y=
2×1
−4±
16+4×1×128
y=
2
−4±
16+512
y=
2
−4±
528
y=
2
−4±
528
y=
2
−4±4
33
y=−2±2
33
y=2(−1±
33
)
Put the value in equation ( 1) and we get,
x=2(−1±
33
)+8
x=−2±2
33
+8
x=6±2
33
Hence, this is the answer.
Step-by-step explanation:
b=l-8
l1 = l + 4
b1 = b+9
area = length × breadth =l1×b1
=(l+4)×(b+9) = lb + 4b +9l +36
given 147 = l1b1 -lb
147 = lb +4b+9l +36 -lb = 4b+9l +36
111= 4b+4l +5l =4(l+b) +5l
substitute b= l-8
111= 4(l+l-8) +5l
111 = 4(2l-8) +5l = 8l -32 +5l = 13l -32
13l = 111+32= 143
l = 11
b=11-8= 3
length =11, breadth = 3