The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides - Noon Academy

The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides

Exercise 6B | Maths | Selina | Solving (simple) Problems (Based on Quadratic Equations)

The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides

Given, a right triangle

$Hypotenuse\text{ }=\text{ }26\text{ }cm$

and the amount of other different sides is

$34\text{ }cm.$

Presently, let believe the other different sides to be

$x\text{ }cm\text{ }and\text{ }\left( 34\text{ }\text{ }x \right)\text{ }cm.$

By utilizing Pythagoras hypothesis,

$\left( 26 \right)2\text{ }=\text{ }x2\text{ }+\text{ }\left( 34\text{ }\text{ }x \right)2$

$676\text{ }=\text{ }x2\text{ }+\text{ }x2\text{ }+\text{ }1156\text{ }\text{ }68x$

$2x2\text{ }\text{ }68x\text{ }+\text{ }480\text{ }=\text{ }0$

$x2\text{ }\text{ }34x\text{ }+\text{ }240\text{ }=\text{ }0$

$x2\text{ }\text{ }10x\text{ }\text{ }24x\text{ }+\text{ }240\text{ }=\text{ }0$

$x\left( x\text{ }\text{ }10 \right)\text{ }\text{ }24\left( x\text{ }\text{ }10 \right)\text{ }=\text{ }0$

$\left( x\text{ }\text{ }10 \right)\text{ }\left( x\text{ }\text{ }24 \right)\text{ }=\text{ }0$

In this way,

$x\text{ }=\text{ }10,\text{ }24$

On the off chance that

$x\text{ }=\text{ }10;\text{ }\left( 34\text{ }\text{ }x \right)\text{ }=\text{ }24$

Or then again

$if\text{ }x\text{ }=\text{ }24;\text{ }\left( 34\text{ }\text{ }x \right)\text{ }=\text{ }10$

Hence, the lengths of the three sides of the right-calculated triangle are

$10\text{ }cm,\text{ }24\text{ }cm\text{ }and\text{ }26\text{ }cm.$

i

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