A 10 metre long rope is to be cut into two pieces and a square is to be made using each. The difference in the areas enclosed must be 1 1/4 square metres. How should it be cut?
answer.
length of the first piece=X
length of the second piece=y
X+y=10______ equation no 1
side of the first square =X/4
side of the second square= y/4
(X/4)2square - (y/4)2square= 1 1/4
x2square/16- y2square/16 =20/16 means 20 by 16
x2square-y2square=20
x2square-y2square=(x+y)(x-y)= 10(x-y)=20
x-y=20/10=2_____equation 2
equation no 1+ equation no 2=
2x=12/2=6
substitute the value of x in equation no 1
6+y=10
y=10-6=4
half answer given
plzz help me to solve this
give me the balance answer
Answers
Answer:
Step-by-step explanation:
Given
A 10 metre long rope is to be cut into two pieces and a square is to be made using each. The difference in the areas enclosed must be 1 1/4 square metres. How should it be cut?
According to question
x + y = 10 --------------(1)
Area of larger square – area of smaller square = 1 1/4 = 5/4
So x^2 – y^2 = 5/4
(x + y)(x – y) = 5/4
10(x – y) = 5/4
(x – y) = 1/8
So 8x – 8y = 1------------(2)
From 1 and 2 we get
x + y = 10 multiply by 8
8x – 8y = 1
So we get
8x + 8y = 80
8x – 8y = 1
16 x = 81
x = 81/16
putting x = 81/16 in 2 we get
8(81/16) - 8y = 1
81/2 - 8y = 1
81/2 = 1 + 8y
81/2 – 1 = 8y
8y = 79/2
y = 79/2 x 1/8
y = 79/16
Therefore the length of the rope after cutting will be 81/16 and 79/16
Length of one piece = x m
Length of other piece = (10 – x) m
Kerala Syllabus 9th Standard Maths Solutions Chapter 3 Pairs of Equations 1
∴ Rope is divided into 6 m and 4