Question

Guys can you please help me with The Question #15 A). and B). of The Factoring for me, please? :)

Answer 1

Answer:

(a)   width = (x - 1)

      length = (7x - 6)

(b)  Area = 350 cm²

     Perimeter = 114 cm

Step-by-step explanation:

Part (a)

Given equation:  $7x^2-13x+6$

⇒ a = 7,  b = -13,  c = 6

Find 2 two numbers that multiply to ac and sum to b:   -6 and -7

Rewrite b as the sum of these 2 numbers:

$\implies 7x^2-7x-6x+6$

Factorize the first two terms and the last two terms separately:

$\implies 7x(x-1)-6(x-1)$

Factor out the common term (x - 1):

$\implies (7x-6)(x-1)$

Therefore:

• width = (x - 1)
• length = (7x - 6)

Part (b)

Substitute the given value of x = 8 into the equations to find the area and perimeter:

$\begin{aligned}x=8cm \implies \textsf{Area} & = 7(8)^2-13(8)+6\\& = 448-104+6\\& = 350 \sf \:\: cm^2\end{aligned}$

$\begin{aligned}\textsf{Perimeter} & = 2(\sf width+length)\\& =2[(x-1)+(7x-6)]\\ & = 2[(8-1)+(7(8)-6)]\\ & = 2[7+(56-6)] \\& = 2(7+50)\\& = 2(57)\\ & = 114 \sf \:\: cm\end{aligned}$

Answer 2

Answer:

See below ~

Step-by-step explanation:

$\textsf {Question 15(A) :}$

$\textsf {Given :}$

$\implies \mathsf {7x^{2} - 13x + 6}$

$\textsf {Splitting the middle term :}$

$\implies \mathsf {7x^{2} - 7x - 6x + 6}$

$\textsf {Grouping common terms :}$

$\implies \mathsf {7x(x - 1) - 6(x - 1)}$

$\textsf {Dimensions are :}$

• $\textsf {Length = (7x - 6)}$
• $\textsf {Width = (x - 1)}$

$\textsf {Question 15(B) :}$

$\textsf {Formula for perimeter :}$

$\implies \mathsf {2 \times (length + width)}$

$\implies \mathsf {2 \times (7x - 6 + x - 1)}$

$\implies \mathsf {2 \times (8x-7)}$

$\textsf {Substitute x = 8 :}$

$\implies \mathsf {2 \times [8(8)-7]}$

$\implies \mathsf {2 \times (64-7)}$

$\implies \mathsf {2 \times 57}$

$\implies \mathsf {Perimeter = 114 cm}$

$\textsf {Now substitute x = 8 in the area formula :}$

$\implies \mathsf {7(8)^{2} - 13(8) + 6}$

$\implies \mathsf {7(64) - 104 + 6}$

$\implies \mathsf {448 - 98}$

$\implies \mathsf {Area = 350 cm^{2}}$