The semi perimeter of a right triangle is 30 cm and its hypotenuse is 26 cm. The other two sides of the triangle are___________
25 cm and 9 cm
20 cm and 14 cm
24 cm and 10 cm
26cm and 8 cm
Answers
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Answer:
3rd option - 24 cm and 10 cm
Step-by-step explanation:
Semi - Perimeter of triangle = 30 cm
Perimeter of Triangle = 60 cm
Hypotenuse = 26 cm
Total length of remaining sides = 60 - 26 = 34 cm
Let perpendicular side = x
Then, base side = 34 - x
Now, we know that,
x, (34 - x) and 26 are Pythagorean Triplets as they form a right angled triangle.
⇒ (x)² + (34 - x)² = (26)² [Pythagoras Theorem]
⇒ x² + 1156 + x² - 68x = 676
⇒ 2x² - 68x = - 480
⇒ 2x² - 68x + 480 = 0 [Forming Quadratic Equation]
⇒ 2x² -48x - 20x + 480 = 0
⇒ 2x (x - 24) -20 (x - 24) = 0
⇒ 2 (x - 24) (x - 10) = 0 [Taking 2 common from second bracket]
⇒ (x - 24) (x - 10) = 0 [Transposing 2 to R.H.S.]
⇒ [x = 24 cm] or [x = 10 cm]
And, (34 - x) = 34 - 10 = [24 cm] or (34 - x) = 34 - 24 = [10 cm]
∴ Hypotenuse = 26 cm
Perpendicular = [24, 10] (ANS.)
Base = [24, 10] (ANS.)