Question

What is the hypotenuse when the longer side is 7 cm greater then shorter side(x)?​

Answer 1

Step-by-step explanation:

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Class 10>>Maths>>Quadratic Equations>>Solutions of Quadratic Equations>>The hypotenuse of a right angled triangl

Question

The hypotenuse of a right angled triangle is 2 centimeters more than the longer of the side containing the right angle. The shorter of the side containing the right angle is 7 centimeters less than the longer side containing the right angle. Find the length of the hypotenuse.

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Solution

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Correct option is A)

Since the hypotenuse of a right triangle is 2 cm more than the longer side of the triangle and the shorter side of the triangle is 7 cm less than the longer side,

therefore, the hypotenuse =x+9, one side =x and the other side =x+7.

From here, you apply Pythagorean theorem:

a2+b2=c2

where

c is length of hypotenuse

a and b are the lengths of the two sides

.

x2+(x+7)2=(x+9)2

x2+(x+7)(x+7)=(x+9)(x+9)

x2+(x2+14x+49)=(x2+18x+81)

2x2+14x+49=x2+18x+81

x2−4x−32=0

Factoring:

(x−8)(x+4)=0

x=−4,8

We can throw out the negative solution leaving:

x=8 cm (short legth)

long legth