Question

Solve the following using the problem-solving strategy.
1) In a right triangle, the hypotenuse is V74 cm. The measure of one of the legs is two
more than the measure of the other. Determine the length of both legs.
Solution:​

Answer 1

Answer:

Let one side be xcm.Since the difference between the two sides is 7cm

∴ the other side=x+7cm

As the given triangle is a right angled triangle with hypotenuse =17cm

By using pythagoras theorem, we get

x

2

+(x+7)

2

=17

2

⇒x

2

+x

2

+14x+49−289=0

⇒2x

2

+14x−240=0

⇒x

2

+7x−120=0

⇒x

2

+15x−8x−120=0

⇒x(x+15)−8(x+15)=0

⇒(x+15)(x−8)=0

⇒x=−15 or x=8

x=−15 cannot be negative

∴x=8

Hence the two sides of the triangle are 8cm and 15cm