Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

The area of a triangle is 20 cm^2, and the altitude is 4 cm greater than the base.Find the length of the base, to the nearest millimeter.

Sagot :

AL2006

Area of any triangle = (1/2) x (base) x (height)

You said ...

Area = 20 cm²
Height = (b + 4)

so we can write the area formula like this,
with everything in centimeters:

                                                          20 = (1/2) x (b) x (b + 4)

Eliminate the parentheses on the right:  20 = (1/2) (b² + 4b)

Multiply each side by  2 :                     40 = b² + 4b

Subtract  40  from each side:              b² + 4b - 40 = 0

Use the quadratic formula to solve this equation,
and you find that

             b = -2 plus or minus 6.633

             b = 4.633
             b = -8.633

The meaningful solution is    base = 4.633 cm

Check:

Area = (1/2) (b) (b+4) =

       (1/2) (4.633) (8.633) =

                (1/2) (40 cm²) = 20 cm²                yay !


We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.