alialwardi06
Answered

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Sagot :

Answer:

n = 14

Step-by-step explanation:

Width of the given right angles triangle = (n + 6) cm

Since, height of this triangle is 10 cm less than the width.

Height = (n + 6) - 10

         = (n - 4) cm

Area of a right angles triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                                  = [tex]\frac{1}{2}(n+6)(n-4)[/tex]

100 = [tex]\frac{1}{2}(n+6)(n -4)[/tex]

200 = n(n - 4) + 6(n -4)

200 = n² - 4n + 6n - 24

200 = n² + 2n - 24

n² + 2n - 224 = 0

n² + 16n - 14n - 224 = 0

n(n + 16) - 14(n + 16) = 0

(n + 16)(n - 14) = 0

n = -16, 14

Since n = -16 is an extraneous solution, so the answer is n = 14.

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