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

6 (3) - 4 + 32

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