Algebraic Expressions and Identities Test

Result

Algebraic Expressions and Identities Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

The perimeter of a triangular field is 6p² − 4p + 9 and two of its sides are p² − 2p + 1 and 3p² − 5p + 3, Find the third side of the field.

A
8p² + 11p − 7

B
2p²+ 3p + 5

C
3p² + 5p − 4

D
5p²− 5p + 9

Solution

erimeter of triangle = Sum of all sides i.e.(6p²−4p+9)=(p²−2p+1) +(3p²−5p+3)+Third side
⇒ Third side = (6p²−4p+9)−(4p²−7p+4)
= 6p² − 4p + 9 − 4p² + 7p − 4
= 2p² + 3p + 5
Question 2
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Ameesha and Prachi love gardening. They water their garden regularly. The length and breadth of Ameesha's kitchen garden are x m and y m respectively. The length of Prachi's kitchen garden is 5 m more than that of Ameesha's garden and the breadth of Prachi's garden is 3 m more than that of Ameesha's garden. Find the difference between the area of Ameesha's kitchen garden and Prachi's kitchen garden.

A
(5x + 8y + 10) m²

B
(3x + 5y − 15) m²

C
(3x + 5y + 15) m²

D
(xy + 3y + 5y + 15) m²

Solution

We have,
Length of Ameesha's kitchen garden= x m
Breadth of Ameesha's kitchen garden= y m
∴Area of Ameesha's kitchen garden = xy m²
Length of Prachi's kitchen garden=(x+5)m
Breadth of Prachi's kitchen garden(y+3)m
∴ Area of Prachi's kitchen garden =(x+5)(y+3)=(xy+3x+5y+15) m²
Difference between area of Ameesha's kitchen garden and Prachi's kitchen garden = xy + 3x + 5y + 15 − xy = (3x + 5y + 15) m²
Question 3
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Amit want to buy a rectangular field whose area is (3a² + 5ab + 2b²)sq. units.

One of its sides is (a+b) units. Find the length of the fence around the field.

A
(10a + 20b) units

B
(4a + 30) units

C
(2a + 2b) units

D
(8a + 60) units

Solution

Area of rectangular field = (3a² + 5ab + 2b²) sq.unit
One side =(a+b) unit To find the other side we factorize 3a² + 5ab + 2b²
∴ 3a² + 5ab + 2b² = 3a² + 3ab + 2ab + 2b² = 3a(a+b) +2b(a+b) =(a+b)(3a+2b)
∴ Other side of rectangle =(3a+2b) unit So, length of fence around the field =2[(a+b)+(3a+2b)] =(8a+6b)units