Answer:
One of the sides is 6 cm and the other is 8 cm
Step-by-step explanation:
Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:
a + b + hypotenuse = 24
a + b + 10 = 24
a + b = 14
b = 14 - a
So now we can right the Pythagorean theorem as follows:
[tex]a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0[/tex]
and from this expression in factor form to be zero a must be 6 or a must be 8.
Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)
or a = 8 (and therefore b = 14 - 8 = 6)
Perimeter of triangle = Sum of all sides.
One side of triangle = 10 cm
Measure of other two sides will be → 24-10
Other two sides sum will be = 14 cm
Let's assume one side as x and other as 14-x
Now hypotenuse is of 10 cm
According to Pythagorean theoram
Hypotenuse² = Perpendicular ² + base²
→ 10² = (x)² + (14-x)²
→ 100 = x² + (14-x)²
(a-b)² = a²+b² -2ab
→ 100 = x² + 196 + x² -28 x
→ 100 = 2x² + 196 - 28x
Taking 2 commen both sides
→ 50 = x² -14x + 98
→ 0 = x² -14x +98-50
→ x² -14 x +48 = 0
Factorising :-
→ x² - 6x - 8x + 48 = 0
→ x( x -6) -8(x -6) = 0
→ (x-6)(x-8) = 0
→ x = 6 or x = 8
So x is 6 or 8
Other two sides of triangle are 6 cm and 8 cm
