QUESTION 1: A mechant has 120 litres and 180 litres of two kinds of oil. He wants to sell the oil by filling the two kinds in tins of equal volumes. Find the greater volume of such a tin. QUESTION 2: Difference between a number and its positive square root is 12 Find the number.

QUESTION 3: A piece of iron rod costs $60. If the rod was 2 meter shorter and each meter cost $1 more, the cost will remain unchanged what is the length of the rod.

QUENTION 4: The sides of an equilateral triangle are reduced by 12 units, 13 units and 14 units respectively and a right-angle triangle is formed Find the length of each side of the equilateral triangle
QUESTION 5: One of the diagonals of a rectangle a 20 cm long. The difference between lts length and its width is 4 cm find the area of the rectangle

1 H C F of 120 and 180 is 2

120/2 = 60

180/2 = 90

Total number of tins = 60+90 = 150

2 16 - √16 =12. So,correct ans is 16.

3 as the new price for each metre is now rs.1 therefore the length of rod should be 60 meters so that it costs rs.60.

and we know the new length is two minus the actual length so,

the actual length of rod=60+2

=62 meters

4 New sides of new Δ=x-12; x-13; x-14.

(x-12) side is the longest side in the right angled Δ

ACCORDING TO THE PYTHAGORAS THEORAM

(x-13)² + (x-14)²= (X-12)²

after opening the brackets...

x² + 169 - 26x + x² + 196 - 28x = x² + 144 - 24x

2x² + 365 - 54x = x² + 144 -24x

2x²- x² + 365 - 144 - 54x + 24x= 0

x² - 30x + 221 =0

x² -17x -13x + 221=0

x(x-17) -13(x-17)= 0

(x-13)(x-17)=0

x-13=0 or x-17=0

x=13 x=17

x ≠13 (because if x is 13 then side (x-13) of Δ would be zero

which is imposiible)

x= 17 units

25

step-by-step explanation:

y + 11 = (1/4)(x + 16)

step-by-step explanation: