Question

the hypotenuse of right triangle is 13cm and the difference between the other two sides is 7cm. find the two unknown sides of the triangle​

Answer 1

Step-by-step explanation:

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• according to Pythagorean triplet, hypotenuse square is equal to square of sum of the other 2 sides
• let one of the side be 'x' then the other side will be '7+x'
• hence, (13)²=(x)²+(7+x)²
• 169=x²+49+x²+14x
• 120=2x²+14x
• 120=2x²+14x
• 2x²+14x-120=0
• x²+7x-60
• x²+12x-5x-60=0
• x(x+12)-5(x+12)
• (x-5)(x+12)
• hence value of x is 5....because the value of length cannot be negative

hence sides are 13,12 and 7

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Answer 2

Step-by-step explanation:

hypotenuse= 13 cm

let the first side be x cm

let the second side be y cm

x-y = 7

y= -(7-x)

y= -7+x

y= x-7

According to the Pythagoras theorem,

(hypotenuse)²= (first side)²+(second side)²

h² = x²+y²

13² = x²+(x-7)²

169= x²+(x)²-2(x)(7)+(7)² {using (a-b)²=a²-2ab+b²}

169= x²+x²-14x+49

169= 2x²-14x+49

2x²-14x-120=0

dividing the whole equation by 2

x²-7x-60=0

x²-12x+5x-60=0

x(x-12)+5(x-12)=0

(x+5)(x-12)=0

x=-5,12

x can't be negative

so, x= 12

y= x-7

y= 12-7

y= 5

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