Question

The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13 cm. Find the other two sides​

Answer 1

Step-by-step explanation:

Given:-

The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13 cm.

To find:-

Find the other two sides of the right triangle ?

Solution:-

Let the base of the right angled triangle be X cm

Then,

The altitude of the triangle = 7 cm less than the base

= (X-7) cm

Hypotenuse of the triangle = 13 cm

By Pythagoras Theorem,

"In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides".

=> 13^2 = X^2+(X-7)^2

=> 169 = X^2+(X^2 -2(X)(7)+(7)^2)

=> 169 = X^2+X^2-14X+49

=> 169 = 2X^2-14X+49

=>2X^2-14X+49 = 169

=>2X^2-14X +49 -169 = 0

=> 2X^2-14X-120 = 0

=> 2(X^2-7X-60) = 0

=> X^2-7X-60 = 0/2

=> X^2-7X-60 = 0

=> X^2+5X-12X-60 = 0

=> X(X+5)-12(X+5) = 0

=> (X+5)(X-12) = 0

=> X+5 = 0 or X-12 = 0

=> X = -5 or X = 12

X can not be negative since it is the length of the side.

=> X = 12 cm

Base of the triangle = 12 cm

Altitude = X-7 = 12-7 = 5cm

Answer:-

The other two sides are 12 cm and 5cm

Base of the right angled triangle = 12 cm

Altitude of the right angled triangle = 7 cm

Used formulae:-

Pythagoras Theorem:-

"In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides".

Answer 2

Answer:

Answer is in attachment....