Question

The sum of length of the perpendicular sides of a right triangle is 26 and it's area is 84 square cm.FInd the product of its perpendicular sides and also find the two perpendicular sides and it's hypotenuse​

Answer 1

Answer:

Given :-

the sum of perpendicular sides of a right triangle is 26 cm

area of right triangle is 84 cm²

To find :-

the product of perpendicular sides ?

the length of the perpendicular sides ?

length of the hypotenuse ?

Formula used :-

area of right triangle = 1/2 base x height

hypotenuse of the right triangle

=>

$\sqrt{?}$

base ^2 + height^2

Solution :-

let base of the right triangle = x cm

let height of the right triangle = y cm

x + y = 26 .. eq. 1

ATQ

1/2 x X x Y =84

X x Y = 84 x 2

X x Y = 168 cm... eq. 2

NOW,

from eq.(2)

x+y =168

x= 168/y

put the value of x = 168 /y in eq. (1).

x + y = 26

168/y + y =26

168 /y + y = 26

168 + y^2 / y = 26

168 + y^2 =26 y

y ^2 - 26y + 168=0

when y = 14 cm

then x :-

x + y = 26

x = 26 - 14

x = 12 cm

when y = 12 cm

then x :-

x + y = 26

x = 26 - 12

x = 14 cm

therefore,

base of right triangle = 12cm or 14cm

also height of right triangle = 12cm or 14cm .

hypotenuse = {\sf \:\sqrt{{base}^{2} + {height}^{2}}}

hypotenuse = \sf\: \sqrt{ {12}^{2} + {14}^{2} }

hypotenuse = {\sf\:\sqrt{144 +196}}

hypotenuse = {\sf\:\sqrt{340 }cm}

here , I have taken base as 12 cm and height as 14 cm because triangle is right triangle . sides can't be equal .

we can also take base as 14 cm and height as 12 cm . but we can't take both side same .