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Levart [38]
3 years ago
8

The hypotenuse of a right triangle is 5cm long the longer leg is 1cm longer than the shorter leg find the side lengths of the tr

iangle
Mathematics
1 answer:
Anvisha [2.4K]3 years ago
5 0

Answer:

<em>Shorter leg=3</em>

<em>Longer leg=4</em>

Step-by-step explanation:

<u>Equations</u>

In a right triangle, Pythagora's Theorem is satisfied. Being a the hypotenuse, b and c the legs of the triangle, then:

a^2=b^2+c^2

Let's call

x=the shorter leg of the triangle

The longer leg is 1 cm longer than the shorter leg, thus:

x+1=the longer leg.

Since the hypotenuse is 5 cm long:

5^2=x^2+(x+1)^2

Operating:

25=x^2+x^2+2x+1

Swapping sides and simplifying:

2x^2+2x+1=25

Subtracting 25:

2x^2+2x-24=0

Dividing by 2:

x^2+x-12=0

Factoring:

(x-3)(x-4)=0

We have two possible solutions:

x=3, x=4

The longer leg is x+1.

If x=3, x+1=4

If x=4, x+1=5. This solution is not valid because one leg would be equal to the hypotenuse.

Thus, the solution is:

Shorter leg=3

Longer leg=4

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