Math question?

Question

I really need help with this question. This is a grade 10 math question, its something about the "Quadratic Formula"
"A photo framer wants to place a matte of uniform width all around a photo. The area of the matte should be equal to the area of the photo. The photo measures 40 cm by 60 cm. How wide should the matte be?"
Thanks to whoever answers this ^__^

Answer 1

Let the width of the matte be w

Then the total area of the photo + matte

= (40+2w) * (60+2w)

= 2400 + 200w + 4w^2

But we know that the area of photo = area of matte

That means area of photo + matte = 2 * area of photo
= 2*40*60
=4800

Therefore
2400 + 200w + 4w^2 = 4800

or

4w^2 + 200w - 2400 = 0

Dividing by 4
w^2 + 50w - 600 = 0

This can be factorized into
(w-10)* (w+60) = 0

So, w = 10 or w = -60

But w cannot be negative.

So, width of the matte = 10

Answer 2

Photo area : 2400 mm².

Photo area and border can be given by:
(40 + x) * (60 + x) = 2400 * 2 mm²
(40 + x) * (60 + x) = 4800 mm²
2400 + 40x + 60x + x² = 4800 mm²
x² + 100x + 2400 - 4800 = 0
x² + 100x - 2400 = 0

Use formula : [-b ± √(b² - 4*a*c)] / 2a
-100 ± √(100² - 4*1*-2400) / 2(1)
x = 20 or x = -120
Taking positive value.
So x = 20 mm. Now add this to picture length and width.
40 + 20 = 60 mm.
60 + 20 = 80 mm.
→ 20mm is the extra lenght and width.
Border thickness = 20/ 2 mm
Border thickness = 10 mm

Answer 3

Photo = 40 cm * 60 cm = 2400 cm^2
matt area = 2400 cm^2

matt area + photo area =
2400 cm^2 + 2400 cm^2 =
4800 cm^2

Since the area of the photo is covered, if we subtract the photo area from the matt area + photo area,
we get 2400 cm^2, which is the required area.

Solve for:
(40 + 2x) cm * (60 + 2x) cm = 4800 cm^2

2x will give us x = the width on each side
FOIL
(2400 + 80x + 120x + 4x^2 ) cm^2 = 4800 cm^2
2400 + 200x + 4x^2 = 4800
4x^2 + 200x - 2400 = 0

Now use the quadratic equation:

a = 4
b = 200
c = -2400

x = {-b +/- sqrt(b^2 - 4ac)} / 2a
.

Answer 4

Let border be x cm
Area of photo = 40 x 60 = 2400 cm²
Area of border = 2400 cm²
2x.(40 + 2x) + 120 x = 2400
4x² + 200x - 2400 = 0
x² + 50x - 600 = 0
(x - 10).(x + 60) = 0
x = 10 is acceptable answer.
Border width = 10 cm

Answer 5

area of the photo = 40 x 60
= 2400cm^2
let width of matte= y

lenght of matte=60+2y
breadth of matte=40+2y
area=(60+2y)(40+2y)
=4y^2+200y+2400
so,
4y^2+200y+2400-2400=area of matte(2400)
4y^2+200y=2400


Try solving this quadratic equation now, i've made it much easy for you.
Hope that helps.

Answer 6

Answer is 40 * 60 = 2400

Answer 7

why cant u do ur homeworks by ur self??

im also in grade 10 and i know the answer .. im 16 ..

but it wouldnt be nice if i do other people's homeworks :S