PLS HELP ASAP!!!! the base of a triangle is 103cm more than its height. if the hypotenuse of the triangle is 205cm what are the base and height of the triangle?
Answers
Given :- The base of a triangle is 103cm more than its height. if the hypotenuse of the triangle is 205cm ?
Solution :-
Let us assume that, height of the right angled triangle is x cm .
so,
→ Base = (x + 103) cm .
then, using pythagoras theorem, we get,
→ Base² + perpendicular² = hypotenuse²
→ (x + 103)² + x² = 205²
→ x² + 103² + 206x + x² = 205²
→ 2x² + 206x = 205² - 103²
→ 2x² + 206x = (205 + 103) * (205 - 103)
→ 2x² + 206x = 308 * 102
→ 2(x² + 103x) = 31416
→ x² + 103x - 15708 = 0
→ x² - 84x + 187x - 15708 = 0
→ x(x - 84) + 187(x - 84) = 0
→ (x - 84)(x + 187) = 0
→ x = 84 or (-187) .
since side a ∆ cant be negative.
therefore,
- Height of the triangle = x = 84 cm .
- Base of the triangle = (x + 103) = 84 + 103 = 187 cm .
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