Question

The base of a triangle exceeds the height by 3 cm if the area is 170 cm² what is the length of the base and the height of the triangle

Answer 1

Hey there!!

How do we find the area of a triangle?

Ans - Formula = ( 1 / 2 ) ( base ) ( height )

In the question, it states the base exceeds the height by 3 cm

Let's take the height as ' x '

The, the base of the triangle would be ' x + 3 '

It's area = 170 cm²

Let' get this into an equation :

( 1/2 ) ( x ) ( x + 3 ) = 170

... ( x / 2 ) ( x + 3 ) = 170

... ( x² + 3x / 2 ) = 170

Multiplying by 2 on both sides

... x² + 3x = 340

Subtract 340 on both sides

... x² + 3x - 340 = 0

We can write this as

... x² - 17x + 20x - 340 = 0

... x ( x - 17 ) + 20 ( x - 17 ) = 0

... ( x + 20 ) = 0

... ( x - 17 ) = 0

... x = -20

... x = 17

As the value can not be in negatives, we take x as 17

The value of height = 17 cm

The value of the base = 20 cm

Hope my answer helps!!

Answer 2

Let's consider the length of the height of the triangle to be $h$ and the length of the base of the triangle to be represented by $b$.

From the information in the problem, we can say that:

$b = h + 3$

Now, we have the lengths of the base and height represented as expressions. We can use the formula for area of a triangle ($A = \frac{1}{2} b h$) and set it equal to 170 to find the lengths of the base and height, as shown below:

$\frac{1}{2} (h + 3) (h) = 170$

• Substitute in our expressions for $b$ and $h$

$\frac{1}{2} (h^2 + 3h) = 170$

• Apply the Distributive Property

$h^2 + 3h = 340$

• Multiply both sides by 2 to remove the $\frac{1}{2}$ on the left side of the equation

$h^2 + 3h - 340 = 0$

• Subtract 340 from both sides of the equation

$(h - 20)(h + 17) = 0$

• Factor

$h = -20, 17$

• Apply the Zero Product Property, set both factors equal to 0, and solve for $h$.

$h = 17$

• $h$ cannot equal to -20 because you cannot have a negative value for a height

We have figured out that the height of the triangle is 17 cm. To find the base, we can substitute the value we found for the height into the equation. From this equation (which was $b = h + 3$, from above), we can find that the base of the triangle is 20 cm (b = 17 + 3 = 20).