Question

Hypotenuse of a right triangle is 1 unit greater than two times the base. Altitude is 7 units greater than the base find the sides of the rectangle​

Answer 1

Answer:

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Step-by-step explanation:

let for a certain right angled triangle it's altitude be x.units,its base be y.units and it's hypotenuse be z.units

so according to first condition

z=2y+1 (1)

so according to second condition

x=y+7 (2)

so as it is a right angled triangle

applying pythagoras theorem

we get

x²+y²=z²

(y+7)²+y²=(2y+1)²

y²+49+14y+y²=4y²+1+4y

ie 2y²+14y+49=4y²+4y+1

so thus ie

2y²-10y-48=0

Dividing by 2 on both sides we get

y²-5y-24=0

y²-8y+3y-24=0

y(y-8)+3(y-8)=0

ie (y-8)(y+3)=0

so y=8 or y=-3

but as dimensions length are never negative

y=-3 is absurd

hence y=8

substitute value of y in (1) and (2)

We get

x=15

z=17

Hence for given right angled triangle

Its altitude is 15 units,its base is 8 units and that of its hypotenuse is 17 units