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Which equation would best solve the problem?
The height of a triangle is 6m more than its base. The area of the triangle is 56m2. Find the length of the base.
A. 56=1/2(x)(x+6)
B. 56=1/2 (x2 +6)
C. 56=x(x+6)
D. 56=x2+6
The height of a triangle is 5m less than its base. The area of the triangle is 42m2. Find the length of the base.
A. 8 m
B. 7 m
C. 12 m
D. 11 m
Added 3+ months ago:
I've got 5 questions. Question 3, Holly has a rectangular garden that measures 12m
Added 3+ months ago:
Please hurry thank you so much :)
To solve the first problem, you need to know the formula to find out area first.
Area = (1/2)* base*height
So, when you let base as x m then, definitely height becomes (x+6)m. So substitute the values in above formula and you'll get the answer.
I think A is correct.
When it comes about the second problem, the formula remains same. But you need to use logic.
Let the base be x m, then the height becomes (x-5)m. Substitute the values and solve to get answer.
42 = (1/2)*x*(x-5)
84 = x^2 - 5x
x^2 - 5x - 84 = 0
Now we have to factorize,
x^2 - 12x + 7x - 84 = 0
x(x-12) + 7(x-12) = 0
(x-12)*(x+7) = 0
Either, x - 12 = 0 or, x + 7 = 0
x = 12 x = -7
Since, length can never be negative, -7 is rejected
So, the correct answer is C. 12 m
