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The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base? Question 2 options: 7 m 8 m 14 m 15 m

Verified Answer :

apologiabiology

h=6+b
a=(1/2)bh
a=56

56=(1/2)bh
times 2 both sides
112=bh
h=6+b

112=b(6+b)


112=b²+6b


minus 112 both sides


0=b²+6b-112


factor


what 2 numbers multily to get -112 and
add to get 6


-8 and 14


0=(b-8)(b+14)


set to zero




b-8=0


b=8




b+14=0


b=-14


false, measures can't be negative




base=8


h=6+b


h=6+8


h=14








height=14


base=8



aksnkj

Use the formula for the area of a triangle. The length of the base will be 8 metres.

Given,

The area of triangle is 56 square meter.

Let the length of base be x meter.

So, the height of the triangle will be x+6 meters.

We have to calculate the length of the base.

How to get the area of a triangle?

We know that Area of triangle is,

\(A=\dfrac{1}{2} \times Base\times Height\)

\(56=\dfrac{1}{2}\times x\times (x+6)\)

\(112=x^{2} +6x\)

\(x^{2} +6x-112=0\\\)

How to solve a quadratic equation?

On solving the above quadratic equation by middle term split method we get,

\(x^{2} +14x-8x-112=0\\\)

\(x(x+14)-8(x+14)=0\)

\((x+14)(x-8)=0\)

When

\(x+14=0\\\)

\(x=-14\)

And when

\(x-8=0\\\)

\(x=8\)

Since side cannot be negative so neglecting the negative value of x, the final value of x will be 8.

Hence the correct option is B. 8 meter.

For more details about triangles, follow the link:

https://brainly.com/question/15442893

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