The base of a triangle is (x + 7) inches long. The height of the triangle is (x - 4) inches long. If the area of the triangle is 13 square inches, what is the value of x.

x = 6, and x = - 9

Step-by-step explanation:

Area of a triangle = 1/2 base * height = 13 square inches

Slot in the values of the base and height

13 = 1/2 (x + 7) * (x - 4)

Expand

13 = 1/2 (x^2 - 4x + 7x - 28)

collect like terms

13 = 1/2 (x^2 + 3x - 28)

cross multiply

13*2 = x^2 + 3x - 28

26 = x^2 + 3x - 28

Subtract 26 from both sides

0 = x^2 + 3x - 28 - 26

0 = x^2 + 3x - 28 - 54

rearrange

x^2 + 3x - 54 = 0

Two numbers which when multiplied gives - 54 and when summed gives 3 are - 6 and 9

x^2 - 6x + 9x - 54 = 0

x (x - 6) + 9 (x - 6) = 0

(x - 6) (x + 9) = 0

x - 6 = 0

x = 6

x + 9 = 0

x = - 9