algebra 2?

Question

theres this extra credit problem im doing and i reallllly wanna get it right but i forget what to do :( its about a triangle, the area = 35 ft squared, and i need to find the base and heigt. h=b+3. i think so far its 35=1/2(b)(b+3)

please help!

Answer 1

You are on the right track.
Since the area of a triangle is .5bh, you get the equation you wrote there.

So now you do the algebra.
35=(b^2+3b)/2
multiply both sides by 2
70=b^2+3b
Subtract both sides by 70
0=b^2+3b-70
factor to solve for b
0=(b+10)(b-7)
so b can be either -10 or 7, but since base is length and length has to be positive, b must be 7.

So then you go back to your equation for height to get
h=7+3=10.

If you compute the area of a triangle with base 7 and height 10, it comes out to 35.

Answer 2

area is b x height div 2 so b x h over 2 = 35 so b x h has to be equal to 70 h is higher than b by 3 so h -3 = b so you get the 2 equations b x h = 70 and h - 3 = b so you plug it into the other equation and get (h - 3) x h = 70 h = 10 since 10 - 3 ( 7) x 10 = 70 and then you plug h = 10 for any equation left so 10 x 7 = 10
10 = height base = 7

Answer 3

So far so good. 35= 1/2 (b^2+3b)
70= b^2+3b you have multiplied by 2
0= b^2+3b-70
0= (b+10)(b-7)

Either b+10=0 or b-7=0
b= -10 or b=7

Since a side cannot be negative, b must be 7
height=b+3=7+3=10

Checks: area= 1/2(7)(10)=35

Answer 4

A = (1/2) b h
A = (1/2) (b) (b + 3)
35 = (1/2) (b) (b + 3)
70 = b² + 3b
b² + 3b - 70 = 0
(b + 10)(b - 7) = 0
b = 7 ft (accept +ve value)

35 = (1/2) (7) h
70 = 7 h
h = 10 ft

Answer 5

35=1/2b(b+3)
70=b(b+3)
70=b^2+3b
b^2 + 3b - 70 = 0
(b-7)(b+10) = 0

therefore b=7ft (base of the triangle)

h=b+3 = 10ft (height of the triangle)

Peace!

Answer 6

You are right. since the formula of the area = (b)(h)/2 and h=b+3 you just need to solve that equation for b and then plug it back into h=b+3 to get h