Question

The length of the base of a triangle is 4 cm smaller than the length of its altitude. The

area of the triangle is 96 cm2. The length of the base is​

Answer 1

Answer:

if the base is assumed to be the altitude is H = b + 4 .

1/2 ( a + b ) = 96.

b square + 4b - 192 = 0

solving this equation for the positive value we get B = 12 cm and hence h = 16 cm

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Answer 2

The length of the base is 12 cm.

Given,

The length of the base of a triangle is 4 cm smaller than the length of its altitude. The area of the triangle is 96 cm2.

To Find,

The length of the base is =?

Solution,

We can solve the question as follows:

It is given that the length of the base of a triangle is 4 cm smaller than the length of its altitude. The area of the triangle is 96 cm2. We have to find the length of the base.

$Area = 96\: cm^{2}$

Let the length of the altitude be equal to x cm. Then the base will be equal to (x - 4) cm.

$Altitude = x\: cm\\Base = (4 - x)\: cm$

Now,

The formula for finding the area of a triangle is:

$Area = \frac{1}{2}*Base*Altitude$

Substituting the values in the above formula,

$96 = \frac{1}{2} *(x - 4)(x)$

$96*2 = x^{2} - 4x$

$192 = x^{2} - 4x$

$x^{2} - 4x - 192 = 0$

Now, we will solve the above quadratic equation.

$x^{2} - 4x - 192 = 0$

$x^{2} +12x - 16x - 192 = 0$

$x(x + 12) - 16(x +12) = 0$

$(x - 16)(x + 12) = 0$

$x - 16 = 0, x + 12 = 0$

$x = 16, - 12$

Since it can't be negative, the value of x is 16.

Then, the length of the base will be:

$Base = 16 - 4 = 12\: cm$

Hence, the length of the base is 12 cm.