Find the side lengths of the triangle if

Bryanna Leon

Bryanna Leon

Answered question

2022-04-08

Find the side lengths of the triangle if the hypotenuse of a right triangle is 5 cm long, and the shorter leg is 1 cm shorter than the longer leg.

Answer & Explanation

Ausspruchx807

Ausspruchx807

Beginner2022-04-09Added 6 answers

Pythagorean's Theorem:
c2=a2+b2, where c is hypotenuse of the right triangle; a is base and b is perpendicular of the right triangle.
Let the longer leg is a, the shorter leg is b, and the hypotenuse is c
Given that the hypotenuse of a right triangle is 5cm
We have: c=5cm
As the shorter leg is 1cm shorter than the longer leg, we have:
b=a1
Thus, we have:
(5)2=a2+a2+12a
25=2a2+12a
2a22a24=0
a2a12=0
a24a+3a12=0
(a4)(a+3)=0
a=4 and a=3 (can't be true, as side cannot be negative)
From first equation we have b=3
Hence, Shorter leg=3m, Longer leg=4cm, Hypotenuse = 5cm

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