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Daniel [21]
2 years ago
11

The hypotenuse of a right triangle measures 20cm. The sum of the lengths of the other two sides is 28cm. Find the lengths of tho

se two sides.
Mathematics
1 answer:
scoray [572]2 years ago
3 0

Step-by-step explanation:

<h3>Here, </h3><h3>h = 20cm</h3><h3 /><h3>By question, </h3><h3>p + b = 28cm</h3><h3>or, p = 28 - b</h3><h3 /><h3>Using pythagoras theorem, </h3>

<h3>h^2 =p^2 + b^2</h3><h3>20^2 = (28-b) ^2 + b^2</h3><h3>400 = 28^2 -2x28xb + b^2 + b^2</h3><h3>56b = 784 - 400 + 2 b^2</h3><h3>0 = 2b^2 - 56b + 384 </h3><h3>0 = 2 ( b^2 - 28b + 192)</h3><h3>0 = b^2 - (16 + 12) b + 192</h3><h3>0 = b^2 - 16b - 12b + 192</h3><h3>0 = b (b - 16) - 12 (b - 16)</h3><h3>0 = (b - 16) (b - 12)</h3><h3>Either, </h3><h3>b= 16</h3><h3>Or,</h3><h3>b = 12</h3>

<h3>When b = 16,</h3><h3>p = 28 - 16 </h3><h3> = 12</h3><h3>When b = 12,</h3><h3>p = 28 - 12</h3><h3> = 16</h3>
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