Help with polynomials?

Question

I need some help with the following problems:

1. the base of a triangle is 10m greater than the height. the area is 12m squared. find the height and the base.

2. the base of a triangle is 16cm greater than the height. the area is 40cm squared. find the height and the base

3. the height of a triangle is 5cm less than the base. the area is 42cm squared. find the height and the base

4. the base of a triangle is 9cm less than the height. the area is 35cm squared. find the height and base

5. if the sides a square are lengthened by 4m, the area of a square becomes 100m squared . find the length of a side of the original square.

if not the solution to the problem i would prefer how to set it up to solve it, then i can finish the rest.

thanks!

Answer 1

1). let b = base
h = height.
given that base is 10 m greater dan height
thus, h+10 = b.............eqn 1

1/2b*h(area) = 12

12= 1/2*h(h+10) .......as b = h+10
24 = h(h+10)
24= h^2 + 10h
h^2 + 10h - 24 = 0
this is quadratic in h
solving, we get h=2
and substituting in eqn 1
we get b = 12

all other sums can be solved similarly

Answer 2

1. the base of a triangle is 10m greater than the height. the area is 12m squared. find the height and the base.

bh/2 = A

1) b = h + 10

2) bh/2 = 12
(h + 10)h/2 = 12
h^2 + 10h = 24
h^2 + 10h - 24 = 0
(h + 12)(h - 2) = 0
h = -12, h = 2 {discard negative root}

h = 2
b = 2 + 10 = 12

Check

12 = 2(12)/2
12 = 12

5. if the sides a square are lengthened by 4m, the area of a square becomes 100m squared . find the length of a side of the original square.

(s + 4)^2 = 100
s^2 + 8s + 16 = 100
s^2 + 8s - 84 = 0
(s - 6)(s + 14) = 0
s = 6, s = -14 {discard negative root}

Check

(6 + 4)^2 = 10^2 = 100

Answer 3

1. the base of a triangle is 10m greater than the height. the area is 12m squared. find the height and the base
12 squared = 12 * 12 (anything squared is itself times itself)
10 * Y = (12 *12)

2. the base of a triangle is 16cm greater than the height. the area is 40cm squared. find the height and the base
(X+16) * Y = (40 * 40)

3. the height of a triangle is 5cm less than the base. the area is 42cm squared. find the height and the base
X * (Y-5) = (42 *42)

4. the base of a triangle is 9cm less than the height. the area is 35cm squared. find the height and base
(X-9) * Y = 35 squared

5. if the sides a square are lengthened by 4m, the area of a square becomes 100m squared . find the length of a side of the original square.
(X+4) * 4 = 100 squared

Hope this helps!

Answer 4

Area of triangle A=1/2 base x height

#1 Area=12x12 =1/2bh solve for an unknown and use it in
b=10+h

#4 (side +4)^2=100^2