Question

The altitude of a right triangle is 4cm more than its base. If its hypotenuse is 20cm, find the other two sides.

Answer 1

Answer:

Height is 16cm and base is 12cm. SEE ↓

Step-by-step explanation:

Given : hypotenuse=20cm

let base be =' x 'cm

therefore, height= (x+4)cm

Now, using Pythagoras theorem,

=>height ² + base² = hypotenuse ²

=>(x+4)² + x² = 20²

=> x² + 16 + 8x + x² = 400

=>(2x² + 8x - 384) = 0

=>x² + 4x - 192 = 0. [dividing both sides by 2 ]

=>x²+16x-12x-192 = 0

=>x(x+16)-12(x+16)=0

=> (x-12)(x+16)=0

Now,

=>(x-12)=0

=>x=12 ----------> point no. 1

OR,

=>(x+16)=0

=>x = -16 ----------> point no. 2

therefore, there are two values as it's a quadratic equation,... which fits the best is the answer.

By trial and error method , if we take point one ..

then the values are =

x=12cm

x+4= 16cm

Verification :-

=>12² + 16² = 20²

=>144+256=400

=>400=400

hence , point one is the correct option and no need to try point 2.

ANS => HEIGHT = 16cm, BASE=12cm.

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