Question

which of the following trinomials can be represented by a rectangle?
a. y^2 + 3y +12
b. y^2 + 12y + 5
c. y^2 +8y + 15
d.y^2 + 14y +3

Answer 1

Answer:

✏️${\huge{\blue{\mathbb{\underline{\underline{Question}}}}}}$✏️

Which of the following trinomials can be represented by a rectangle?

$a. {y}^{2} + 3y +12$

$b. {y}^{2} + 12y + 5$

$c. {y}^{2} +8y + 15$

$d.{y}^{2}+ 14y +3$

✏️${\huge{\blue{\mathbb{\underline{\underline{Important\ point}}}}}}$✏️

For being a rectangle:

A trinomial have to be two different terms;

One as length of the rectangle.

Second as breadth of the rectangle.

✏️${\huge{\blue{\mathbb{\underline{\underline{Solution}}}}}}$✏️

So, let's factorise each trinomial to check which is a rectangle;

$a. {y}^{2} + 3y +12$

✈️This term can't be factorise as we don't get any factors by multiplying first and last term✈️

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$b. {y}^{2} + 12y + 5$

✈️This term also can't be factorise as here also we don't get any factors by multiplying first and last term✈️

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$c. {y}^{2} +8y + 15$

$=>{y}^{2}+5y+3y+15$

$=>y(y+5)+3(y+5)$

$=>(y+5)(y+3)$

As, here we get two terms as one as length (y+5) and one as breadth (y+3);

So,this trinomial is represented by a rectangle.

${\pink{\mathfrak{Option\ c\ is\ correct}}}$

Answer 2

From the given question the correct answer is:

$c. y^2 +8y + 15$

the trinomials can be represented by a rectangle.

Solution:

we know that,

A trinomial have to be two different terms One as length of the rectangle Second as breadth of the rectangle.

Now we have to check wheather it is trinomial or not

for this  let's factorise each trinomial to check which is a rectangle.

$y^{2} +3y+12$

 $y^{2} +3y+12$ term can't be factorise as we don't get any factors by multiplying first and last term

$y^{2} +12y+15$

$y^{2} +12y+15$ also can't be factorise as here also we don't get any factors by multiplying first and last term.

$y^2 +8y + 15$

$=y^{2} + 5y+3y+15$

$=y(y+5)+3(y+5)$

$=(y+5)(y+3)$

It can be factorise as here also we don't get any factors by multiplying first and last term.

As, here we get two terms as one as length (y+5) and one as breadth (y+3);

Hence, this trinomial is represented by a rectangle.