Question

Represent the following situation mathematically:
The hypotenuse of a right triangle is 25 cm. We know that the difference in lengths of
the other two sides is 5 cm. We would like to find out the length of the two sides?

Answer 1

x^2+(x+5)^2=25^2
x=15
x+5=20

Answer 2

Answer:-

Let the length of the smaller side be x cm.

Then length of the longer side = ( x+ 5 )

Given length of the hypotenuse = 25 cm

We know that in a right angled triangle

$(hypotenuse) ^{2} = (side) ^{2} + (height) ^{2}$

So,

${x}^{2} + ( {x } + 5) ^{2} = {25}^{2}$

${x}^{2} + {x}^{2} + 10x + 25 = 625$

${2x}^{2} + 10x - 600 = 0$

${x}^{2} + 5x - 300 = 0$

✈︎Value of 'x' from the above equation will give the possible values of length of side of the given right angled triangle.

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