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in Quadratic Equations by (65.5k points)

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

1 Answer

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by (65.2k points)
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Best answer

In ⊥∆ABC, 

∠ABC = 90°. 

AB is altitude, 

BC is base AC is Hypotenuse 

Let Base, BC = x cm. 

if so considered, : 

Altitude AB = (x – 7) cm. 

Hypotenuse AC = 13 cm. 

As per Pythagoras theorem, 

In a right angled ABC, 

AB2 + BC2 = AC2 

(x – 7)2 + (x)2 = (13)2 

x2 – 14x + 49 + x2= 169 

2x2 – 14x + 49 = 169 

2x2 – 14x + 49 – 169 = 0 

2x2 – 14x – 120 = 0 

x2 – 7x – 60 = 0

x2 – 12x + 5x – 6 0 = 0 

x(x – 12) + 5(x – 12) = 0 

(x – 12) (x + 5) =0 

If x – 12 = 0, then x = 12 

If x + 5 = 0, then x = -5 

Positive value, x = 12 

∴ Base, BC = x = 12 cm. 

Altitude, AB = x – 7 = 12 – 7 = 5 cm.

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