Question

1. In a parallelogram a diagonal of the length 20 cm is perpendicular to one of the sides. Find the longer side of parallelogram if its perimeter is 80 cm.

2. The square root of number that is two bigger than k is twice as big as the square root of the number one less than k. What is k?

3. Find two consecutive numbers if the square root of the smaller number is 3 less than the bigger number.

Please give good explanations

Answer 1

1. Let the width be w. The length will be given by:
(80-2w)/2=40-w
given that the diagonal that is perpendicular to one side is 20 cm, the value of the unknown in the above equation will be:
40-w=20
w=20
hence the value of the length will be 40-w=40-20=20 cm

2]The number is (k+2) the square root of this number is √(k+2)
√(k+2)=2√(k-1)
squaring both sides gives
(k+2)=4(k-1)
k+2=4k-4
4k-k=4+2
3k=6
k=2

3] let the smaller number be x, the bigger number is x+1
√x=x+1-3
√x=(x-2)
x=x²-4x+4
0=x^2-5x+4
solving the quadratic we get:
x=1 or x=4
the first number is either 1 or 4, the second number is either 2 or 5
but since
√1≠(2-3)
then the answer is:
first number is 4, second number is 5