Question

30. The perpendicular side of a right triangle are 2cm and 4cm respectively
(a)calculate the hypotenuse to the nearest millimeter
(b) Find the perimeter of the triangle

please give the answer with explanation fast....​

Answer 1

Answer:

Step-by-step explanation:

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:

a  

2

+b  

2

=c  

2

 

where

c is length of hypotenuse

a and b are the lengths of the two sides

.

x  

2

+(x+7)  

2

=(x+9)  

2

 

x  

2

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

x  

2

+(x  

2

+14x+49)=(x  

2

+18x+81)

2x  

2

+14x+49=x  

2

+18x+81

x  

2

−4x−32=0

Factoring:

(x−8)(x+4)=0

x=−4,8

We can throw out the negative solution leaving:

x=8 cm (short leg)

long leg =x+7=8+7=15 cm

hypotenuse =x+9=8+9=17 cm  

Hence, the length of the hypotenuse is 17 cm