Question

The area of the triangle is 42 square units. If the base is 10 units less than four times of its height. What is the length of its base?

Answer 1

Length of its base

Step-by-step explanation:

Step 1:

Let height =x,  Base=4x - 10

Step 2:

1/2 x base x height = Area of Triangle

Step 3:

As area of triangle is given so,

1/2 (4x-10)x =42

After simplifying the above equation we get,

(2x-5)x=42

Step 4:

2$x^{2}$ - 5x - 42=0

Now using factorization,

2$x^{2}$+ 7x - 12x - 42= 0

Step 5:

Taking common,

x(2x+7) - 6(2x+7)=0

x-6=0,   2x+7=0

x=6 and x= -7/2

Step 6:

We take x = 6 and put it in equation where the existing

Base= 4x-10,

Base=4(6)-10

Base=24-10

Base=14.

Final Answer:

Base=14,  Height=6.

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