Can someone help me with these two math problems?

1) The formula for the area of a triangle is 1/2 * Base * Height.

Let's call the base b. WE know the height is three times the base, so the height is 3b, and we can put that into our formula.

1/2 * Base * Height

= 1/2 * b * 3b

Finally, we know the area is 12 cm^2. So,

12 = 1/2 * b * 3b

1/2 * 3b^2 = 12

3b^2 = 24 (because dividing by 1/2 is the same as multiplying by 2)

b^2 = 8

b = +/- √8

b = +/- √4*2

Base = +/- 2√2.

Height = 3 * +/- 2√2.= +/- 6√2.

12. Dimitri's patio will be a rectangle, so its area is A = length * width

A = 12 * 8 = 96 square feet

Each brick is 3inches * 3 inches = 3/12 feet * 3/12 feet = 1/4 * 1/4 = 1/16 square feet.

Assuming we can cut the bricks to make them fit the space, the number of bricks needed will be the total area/area of each brick

= 96/(1/16)

But dividing by a fraction is the same as multiplying by the same fraction turned upside down (the inverse), so

Num Bricks = 96 * 16/1 = 1536.

Each brick costs $2, so the total price is 2 * 1536 = $3072

1.

area of triange: base * height/2

let the base length be x cm

12 = x * 3x/2

24 = 3x^2

8 = x^2

x = (+-) 2 sqrt(2)

since length can only be positive, the base is 2 sqrt(2) cm

calculate height accordingly

2.

you can make 12 x 6 feet with bricks laying the same direction

the number of bricks you'd need is (12/3*12) * (6/3*12) = 8*144

the remaining 12*2 would need the same number of bricks as 12*3 anyway, so that's 4*144=576 more.

together, he's need 1728 bricks, making that $3456

area = 1/2 h b = 12 cm^2

hb = 24

h = 3 b

3 b^2 = 24

b^2 = 8

b = 2 sqrt(2)

h = 6 sqrt(2)

2.

area = 12 x 8 ft^2 = 96 ft^2

surface area of brick = 3/12 * 3/12 ft^2 = 9/144 ft^2

number of bricks = 96 / (9/144) = 96 * 144/9 = 32 * 48 =1536 bricks

at $2 a brick that is $2 * 1536 = $3072

1) let b = base

then height = 3 x base = 3b

area of triangle = (1/2)hb

12 = (1/2) 3b (b)

24 = 3b^2 <--- multiplied both sides by 2

8 = b^2 <-- divided both sides by 3

b = sqrt(8)

b = 2sqrt(2)

So, height = 3b = 3 x 2 sqrt(2) = 6 sqrt(2),

and base = 2 sqrt(2)

2) Area of pave = 12 ft x 8 ft = (12 ft x 12in/ft) x (8 ft x 12 in/ft) = 13824 in^2

Area of brick = 3 in x 3 in = 9 in^2

So, # of bricks in the pave = 13824 in^2 / 9 in^2 = 1536 bricks

Total cost = 1536 bricks x $2 per brick = $3072.

Area of triangle = (1/2) (base)( height)

the height (h) is three time longer than the base (b)

h = 3b

Area = 12 cm

12 cm = 1/2 (bh) = (1/2)(b)(3b) = (3/2)b^2

12 = 3/2 b^2 --> 24 = 3b^2

8 = b^2

b= 2sqrt(2)

h = 3b = 3(2sqrt(2)) = 6sqrt(2)

try #2

good luck

1)

A=1/2 bh

h=3b

12=1/2b x 3b

12 = 3/2 b^2

8 = b^2

4 x 2 = b^2

2 times square root of 2 = b

2.8 cm = b

base = 2.8 cm

height = 8.4 cm

2)

96 sq feet = Area of Patio (I don't think it's a piano..lol!)

.25 x .25 = area of each brick = .0625 sq feet/brick

96/.0625 = 1536 bricks needed

cost = 2 x 1536 = $3,072

"The area of a triangle is 12 cm."

area = b×h/2 = 12 cm²

"The height is three times longer than the base."

h = 3b

b × (3b)/2 = 12

3b² = 24

b = 2√2

h = 6√2

1) 1/2 bxh = 12 h=bx3

bxh = 24

bxbx3=24

bxb=8

b= the square root of 8?

2)needs 12 bricks so $24

Evaluate the following expression for x = 1/2 and y = 3/4: xy/3 + 1 xy=(1/2)(3/4) xy/3= (3/8)/3=9/8 xy/3+1= 9/8 +1= 17/8 = 2.125 2.) solve for x: -3x - 1 = -4 -3x = -4+1 -3x = -3 x=1

1) h=3b, (bh)/2=12, bh=24

3b^2=24, b^2=8, base=2times the sqrt. of 2.

height=3(2^(3/2)), h=6times the sqrt. of 2.

2.) pretty sure someone else did it but its a patio not piano