Question

The sum of the length of the perpendicular sides of right triangle is 26 cm and it's area is 84 sqcm what is the product of perpendicular sides

Answer 1

Answer:

the sum of perpendicular sides of a right

triangle is 26 cm

area of right triangle is 84 cm2

lo find-

area of right triangle = 1/2 base x height

hypotenuse of the right triangle

V?

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 Xx Y =84

XxY = 84 x 2

X xY = 168 cm... eq. 2

NOW,

from eq.(2)

X+y =168

X= 168/y

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

168/y+y =26

168 /y +y= 26

168 + y^2 /y = 26

168+yA2/y = 26

168+y2 =26 y

y 42 - 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.