Find the lengths of the sides of a right triangle if the hypotenuse 10

kolonelyf4

kolonelyf4

Answered question

2021-11-12

Find the lengths of the sides of a right triangle if the hypotenuse 10 centimeters longer than the shorter leg and 5 centimeters longer than the longer leg.

Answer & Explanation

Rosemary McBride

Rosemary McBride

Beginner2021-11-13Added 10 answers

Formula used:
a) In a right triangle square hypotenuse is equal to the sum of the squares of the other two sides.
If hypotenuse is z, longer side is y and smaller side be x, then z2=x2+y2
b) Factorization method of a quadratic polynomial.
The general quadric equation is
ax2+bx+c=0; a, b, cReal numbers and a0
In quadratic factorization using splitting of middle term which is x term is the sum of the two factors and product is equal to last term.
Step 2
Let the smaller leg be x.
Longer leg by y.
Hypotenuse be z.
According to the problem, hypotenuse is 10 cm longer than the smaller leg.
Therefore,
1) z=10+x
And hypotenuse is 5 cm is longer than the shorter leg.
Therefore,
2) z=5+y
From (1) and (2),
10+x=5+y
y=105+x
y=5+x
Step 3
We know that, in aright angled triangle, z2=x2+y2
(x+10)2=x2+(x+5)2
x2+20x+100=x2+x2+10x+25
x2+20x+100=2x2+10x+25
2x2x2+10x20x+25100=0
x210x75=0
x215x+5x75=0
x(x15)+5(x15)=0
(x15)+(x+5)=0
(x15)=0 or (x+5)=
x=15 or x=15
Length is always positive, therefore x=15
Therefore, smaller g(x)=15 centimeters.
Hypotenuse (z)=10+15=25 centimeters.
Longer (y)=z5=255=20 centimeters.
Step 4
For a give right triangle,
Smaller g=15 centimeters.
Longer g=20 centimeters.
Hypotenuse =25 centimeters.

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