Question

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle.

Answer 1

SOLUTION :  

Given :  

Hypotenuse a right ∆ = 13 cm and  

Let the base of a right ∆ be x cm

Height a right ∆ = (x - 7) cm

By Pythagoras theorem, H² = P² + B²

13² = (x -7)² + x²

x² + (x - 7)² =13²

x² + (x² + 49 - 14x) = 169

[(a - b)² = a² - 2ab + b²]

2x² - 14x + 49 - 169 = 0

2x² - 14x - 120=0

2(x² - 7x - 60) = 0  

x²- 7x - 60 = 0  

Hence, the required quadratic equation is x²- 7x - 60 = 0 .

By factorisation :  

x²- 7x - 60 = 0  

x² - 12x + 5 x - 60 = 0  

x(x - 12) + 5 (x - 12) = 0  

(x - 12)(x + 5) = 0  

x = 12 or x = – 5  

But length of side of a ∆ can not be negative.

Therefore, x = 12

Base = x = 12 cm  

Height = x - 7 = 12 - 7 = 5 cm

Hence,  the base and height of a right ∆ is 12 cm & 5 cm.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer is explained below!

Hope it helps!



Hypotenuse a right ∆ = 13 cm and  

Let the base of a right ∆ be x cm

Height a right ∆ = (x - 7) cm

By Pythagoras theorem, H² = P² + B²

13² = (x -7)² + x²

x² + (x - 7)² =13²

x² + (x² + 49 - 14x) = 169

[(a - b)² = a² - 2ab + b²]

2x² - 14x + 49 - 169 = 0

2x² - 14x - 120=0

2(x² - 7x - 60) = 0  

x²- 7x - 60 = 0  

Hence, the required quadratic equation is x²- 7x - 60 = 0 .
By factorisation :  

x²- 7x - 60 = 0  

x² - 12x + 5 x - 60 = 0  

x(x - 12) + 5 (x - 12) = 0  

(x - 12)(x + 5) = 0  

x = 12 or x = – 5  

But length of side of a ∆ can not be negative.

Therefore, x = 12

Base = x = 12 cm  

Height = x - 7 = 12 - 7 = 5 cm

Hence,  the base and height of a right ∆ is 12 cm & 5 cm