Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

A 100 m2hay shed is to be extended to give 475 m2of oor space in total, as shown. All angles are right angles. Find the value of x.

Sagot :

MrRoyal

Answer:

[tex]x = 15.[/tex]

Step-by-step explanation:

Given

See attachment for floor space

Required

Find x

The floor can be partitioned into three space.

The dimension and the area of each space is:

Dimension: 10 by 10

[tex]A_1 = 10* 10 = 100[/tex]

Dimension: 10 by x

[tex]A_2 = 10* x = 10x[/tex]

Dimension: x by x

[tex]A_3 = x* x=x^2[/tex]

So, the total area is:

[tex]Area =100 +10x + x^2[/tex]

Given that:

[tex]Area = 475[/tex]

So, we have:

[tex]100+10x+x^2 =475[/tex]

Rewrite as:

[tex]x^2 +10x+100-475=0[/tex]

[tex]x^2 +10x-375=0[/tex]

Expand

[tex]x^2 + 25x -15x -375 = 0[/tex]

Factorize

[tex]x(x + 25) -15(x +25) = 0[/tex]

Factor out x + 25

[tex](x+25)(x-15)=0[/tex]

Solve:

[tex]x = -25\ or\ x = 15[/tex]

x cannot be negative; So:

[tex]x = 15.[/tex]

View image MrRoyal
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.