Question

The perpendicular height of triangle is (2x-5)cm and the base measures (x+3)cm. The area of this triangle is 20cm^2.
Find the length of the base.

Answer 1

Answer:

The length of the base of triangle = 8 cm

Step-by-step explanation:

Given:

• Height of a triangle = (2x - 5) cm
• Base of a triangle = (x + 3) cm
• The area of a triangle = 20 cm²

To find:

• The length of the base of triangle.

Solution:

Here, we will use formula of area of triangle to find the value of x and then substituting the value of x, we will find the length of base of triangle as we are already with the area of a triangle. Putting the values in the formula and then doing the required calculations.

Let's find out...

✰ Area of a triangle = 1/2 × b × h

Where,

b is the base of a triangle.

h is the height of a triangle.

Putting the values in the formula we have:

• 20 = 1/2 × (x + 3) × (2x - 5)
• 20 = 1/2 × x(2x - 5) + 3(2x - 5)
• 20 = 1/2 × 2x² - 5x + 6x - 15
• 20 = 1/2 × 2x² + x - 15
• 20 × 2 = 2x² + x - 15
• 40 = 2x² + x - 15
• 2x² + x - 15 - 40 = 0
• 2x² + x - 55 = 0
• 2x² + x - 55 = 0
• 2x² + 11x - 10x - 55 = 0
• x(2x + 11) - 5 (2x + 11) = 0
• (x - 5) (2x + 11) = 0

Take,

• x - 5 = 0
• x = 5

Now take

• 2x + 11 = 0
• x = - 11/2

So, the value of x is 5 ( we will take positive else the value of length of base will come negative which won't be possible ).

Finally, find out the base of the triangle.

Base of a triangle = (5 + 3) cm

Base of a triangle = 8 cm

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