A square has side length x and a triangle has a base (3x - 2) and height (2x + 4). At what value of x will the two figures have the same area? Show work and explain all steps.

0.73

Step-by-step explanation:

Data obtained from the question include the following:

Length (L) of square = x

Base (b) of triangle = (3x – 2)

Height (h) of triangle = (2x + 4)

Area of square = L²

Area of square = x²

Area of triangle = ½bh

Area of triangle = ½(3x – 2) (2x + 4)

Expand

½ [3x(2x + 4) –2(2x + 4)]

½[6x² + 12x – 4x – 8]

½[6x² + 8x – 8]

3x² + 4x – 4

Area of triangle = 3x² + 4x – 4

Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:

Area of triangle = area of square

Area of triangle = 3x² + 4x – 4

Area of square = x²

Area of triangle = area of square

3x² + 4x – 4 = x²

Rearrange

3x² – x² + 4x – 4 = 0

2x² + 4x – 4 = 0

Solving by formula method

a = 2, b = 4, c = –4

x = – b ± √(b² – 4ac) / 2a

x = – 4 ± √(4² – 4×2×–4) / 2×2

x = – 4 ± √(16 + 32) / 4

x = – 4 ± √(48) / 4

x = (– 4 ± 6.93)4

x = (– 4 + 6.93)4 or (– 4 – 6.93)4

x = 0.73 or –2.73

Since the measurement can not be negative, the value of x is 0.73.

4

step-by-step explanation:

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