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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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