Question

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

Answer 1

Given that The altitude of a right triangle is 7 cm less than its baseAltitude is =   x - 7 cmGiven that hypotenuse = 13cm
Applying Pythagoras theorem,    base2+ altitude2 = hypotenuse2plug the values  we get       x2+ (  x – 7)2 = 132    x2+   x2+ 49 – 14  x = 169    2  x2 – 14  x + 48 – 169 = 0    2  x2 – 14  x  – 120 = 0Divide   by 2 to both side to simplify it    x2 – 7  x  – 60 = 0      x2 – 12  x + 5  x – 60 = 0      x (  x – 12) + 5 (  x – 12) = 0    (  x – 12)(  x + 5) = 0    x – 12 = 0 or   x + 5 = 0    x = 12 or   x = –5length can not negative so that x can not equal to – 5base     x = 12cm altitude = 12 – 7 = 5cm

Answer 2

Let base be x
then altitude = x-7

By pythagoras theorum
13^2 = x^2 +(x-7)^2
169 = x^2 + x^2 +49-14x
169 -49 = 2x^2-14x
120 = 2x^2-14x
2x^2 -14x -120= 0
X^2 -7x - 60 = 0
X^2 -12x+5x -60 = 0
X(x-12) +5 (x-12) = 0
(X-12) (x+5) = 0
X = 12 or x = -5

However sidecof triangle cannot be negative.
Therefore x = base = 12
Altitude = X-7
= 12-7
= 5

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