The height of the triangle is 5 centimeters less than than its base. The area is 42 centimeter square.?

Question

Find the length of the base and the height.

Answer 1

Okay. The answer is 1/2b*h=a
1/2(12)(7)=42
12-5=7
That would be your answer.

Answer 2

ok area of a triangle is 1/2 base times height ->A=1/2bh
we have area, so 42=1/2bh. we can also figure out the base and height. lets let the base be x, so the height is x-5, so 42=(1/2)(x-5)x. so we need to multiply it out, so 1/2(x²-5x), which is equal to 1/2x²-5/2x. so 1/2x²-5/2x=42. we need to get x by itself so we multiply each side by 2 to get rid of the denominators. so x²-5x=84. then we can graph it, and get that x can equal either -7 or 12, and since the length cant be negative, it has to be 12. so the base is 12 and the height is 12-5 or 7. There are other ways to solve x²-5x=84 other than graphing, but graphing is the quickest

Answer 3

The formula for the area of a tiangle is A = .5bh (one-half base times height). You know the height is 5cm less than the base and the area is 42, so you'd have 42 = .5b(b - 5).

Distribute out the parentheses: 42 = .5b^2 - 2.5b . You now have a quadratic equation you need to solve. This will have two possible solutions, of which you want the positive solution, which will be the length of the base.

Answer 4

Height=7
Base=12
A=B*H/2
7*12/2=84/2=42cm2

Answer 5

height = 7
base = 12

you solve the problem by using the triangle area formula ( 1/2 base X height)

use h for height and h+ 5 for base ( you need a constant variable)

then, do...
1/2 (h (h+5)) = 42 (you get what im doing still i hope.. i just plugged it in)

you eventually end up with :
1/2h^2 + 2.5h + 42 = 0 and take out 1/2 so you get:
h^2 + 5h + 84 = 0

then solve by using the quadratic formula, your calculator or mental math

Answer 6

Let B be the base. B-5 is the height. Using the area formula:

.5(B)(B-5)=42

B^2 - 5B -84 = 0

(B-12)(B+7)=0

Rejecting negative answer, B=12, so H=7

Answer 7

the height of the triangle is 7cm
the base is 12cm
7x12=84/2=42 squ. cm