Answer:
see explanation
Step-by-step explanation:
using A = bh with b = 2x + 1 and h = x + 1, then
(2x + 1)(x + 1) = 28 ← expand factors on left
2x² + 3x + 1 = 28 ( subtract 28 from both sides )
2x² + 3x - 27 = 0 ← in standard form
To factorise, consider the factors of the product of the coefficient of the x² term and the constant term that sum to give the coefficient of the x term
product = 2 × - 27 = - 54 and sum = + 3
The factors are - 6 and + 9
Use these factors to split the middle term
2x² - 6x + 9x - 27 = 0 ( factor first/second and third/fourth terms )
2x(x - 3) + 9(x - 3) = 0 ( take out the factor (x - 3) )
(x - 3)(2x + 9) = 0
equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
2x + 9 = 0 ⇒ x = - [tex]\frac{9}{2}[/tex]
however x > 0 ⇒ x = 3
base = 2x + 1 = (2 × 3) + 1 = 7 units and height = x + 1 = 3 + 1 = 4 units
