I just need the equation not the answer

Question

The larger base of a trapezoid is three times as long as the shorter base, and the height of the trapezoid is 2 inches longer than the shorter base. The area of the trapzoid is 70 square inches. What is the length of the shorter base, x?

Answer 1

 Dear Tommy,

 

                                             ___Base_X__

                                             l

                                             l h= X+2

                                         __ l_______________

                                                 Base One=   3X  (three times as big as shorter base)

 

This is an incomplete model.  The sides are missing.  Here is a formula to use as you requested:

 

Area = (Base one  +  Base 2)h             70=  (X+3x)(x+2)

                           2                                        2

 

If I have helped you, please give me a thumbs up.

 

                                                  Susan C.

Answer 2

For a trapezoid, AREA = (1/2)(base1 + base2)*height.  Let x = the length of the shorter base (base1):

• The larger base (base2) is three times as long as the shorter base: base2 = 3x
• The height is 2 inches linger than the shorter base: height = x + 2
• The AREA = 70 in²

 

      AREA = (1/2)(base1+base2)*height

 

Substitute in the equations above for base1, base2, and height in terms of x:

 

      70 = (1/2)(x + 3x)*(x+2)

      70 = (1/2)(4x)*(x+2)

      70 = 2x(x+2)

      70 = 2x² + 4x

      0 = 2x² + 4x - 70

      0 = x² + 2x - 35

 

Solve the quadratic for x  (HINT: Factor it.  One of the solutions is negative and one positive.  Since we can't have a negative length, x equals the positive solution)

Answer 3

x = length of the shorter base

3x is the length of the larger base

x + 2 = height

Area = 70 sqin

 

Area = 1/2(s + l)h

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

= 1/2 (4x^2 +8x)

= 2x^2 + 4x 

 

70 = 2x^2 +4x

0 = 2x^2 + 4x -70