Question

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

Answer 1

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Answer 2

GIVEN :

Altitude of right triangle is 7cm less than its base.

Let the base of right triangle be x cm

Altitude of right triangle be (x - 7)cm

Hypotenuse of right triangle = 13cm

From Pythagoras theorm,

(Hypotenuse)² = (Adjacent)² + (opposite)²

(13)² = x² + (x - 7)²

169 = x² + x² - 2(x)(7) + 7²

169 = 2x² - 14x + 49

2x² - 14x + 49 - 169 = 0

2x² - 14x - 120 = 0

Take out 2 as common factor

2 [ x² - 7x - 60 ] = 0

x² - 7x - 60

Split the middle terms

x² - 12x + 5x - 60 = 0

x(x - 12) + 5(x - 12) = 0

x - 12 = 0 ; x + 5 = 0

x = 12 ; x = -5

Sides won't be negative

Hence, x = 12

Base = x = 12cm

Altitude = x - 7 = 12 - 7 = 5cm

Therefore, the two sides are 12cm and 5cm.