3. The length of the hypotenuse of a right angled triangle is 50mm. Calculate the lengths of the other sides if the perimeter of the triangle is 120mm

Question

The length of the hypotenuse of a right angled triangle is 50mm. Calculate the lengths of the other sides if the perimeter of the triangle is 120mm

Answer 1

The lengths of sides a and b are such that a+b=120-50=70 and so b=70-a. Also a^2+b^2=50^2. Substitute for b: a^2+(70-a)^2=2500; a^2+4900-140a+a^2=2500; 2a^2-140a+2400=0; a^2-70a+1200=0; (a-30)(a-40)=0, so the other two sides are 30mm and 40mm.

Comments

Thank you so much Rod

Answer 2

Given Shortest leg = 50mm
Longest leg = x
Hypotenuse,
x + 10
Pythagorean theorem says,
50^2 + x^2 = (x + 10)^2

Expand the right side,
2500 + x^2 = x^2 + 20x + 100

Cancel x^2 from both sides,
20x = 2500 - 100
20x = 2400

Divide both sides by 20,
x = 2400 / 20
x = 120

Answer,
Shortest leg = 50mm
Longest leg = 120mm
Hypotenuse = 130mm

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Comments

The length of the hypotenuse is given as 50mm, so it cannot be changed to 130mm. The question is simply the 3-4-5 triangle in disguise.