Question

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

Answer 1

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Answer 2

ΔABC has side AB as base, BC as altitude and AC as hypotenuse = 13 cm and ∠B = 90°
Let the altitude BC be x.
So, Base AB = x+7
As ∠B = 90°
Use pythagoras theorem in ΔABC
(AB)² + (BC)² = (AC)²
(x+7)² + (x)² = (13)²
x² + 49 + 14x + x² = 169
=> 2x² + 14x - 120 = 0
=> x² + 7x -60 = 0
=> x² + 12x -5x -60 = 0
=> x(x+ 12) - 5(x+12) = 0
=> (x-5)(x+12)=0
=> (x -5) = 0 and (x+12)=0{ We will neglect x = -12 as length cannot be negative)
So x = 5 cm=BC
and x+7=12 cm=AB