Question

The perimeter of a right triangle is 60 cm .If hypotenou is 25 .find area of triangle .

Answer 1

Answer:

perimeter of right triangle = 60

hypotenuos = 25

LET , X = HEIGHT , Y = BASE , Z = HYPOTENUOS

GIVEN , X+Y+Z = 60 AND Z = 25

SO, X+Y = 60-25

==> X+Y = 35

SO, X = 35-Y ...(1)

BY PYTHAGORAS THOEREM

(H)² = (P)²+(B)²

==> (25)² = (X)²+(Y)²

PUTTING VALUE OF X

==> 625 = (35-Y)²+Y²

==> 625 = 1225+Y²-70Y+Y²

==> 2Y²-70Y + 1225-625 = 0

==> 2Y² - 70Y+ 600 = 0

==> 2(Y²-35Y+300) = 0

==> Y²-35Y+300 = 0/2

==> Y²-15Y-20Y+300 = 0

==> Y(Y-15)- 20 (Y-15) = 0

==> SO, Y = 15 , 20

SO, SIDES ARE 15 AND 20

AREA OF TRIANGLE ==> 1/2×BASE×HEIGHT

==> 1/2×15×20

==> 150 CM²

Answer 2

✨here is your answer ✨

perimeter = 60

let the length of perpendicular = x
so , base = 60-(25+x)

= 35-x

✨ by Pythagoras theram

25² = x² + (35-x)²
625 = 2x² + 1225 - 70x
2x² -70x +600= 0
2x² - 40x -30x + 600 =0
2x(x-20) -30(x-20) =0
so,,
x = 15or 20
if x= 15 = p
b = 20
so, area of triangle = 1/2 b×h
= 150cm²
OR
IF x = 20 , so b = 15 , p= 20
so, area = 150cm²

✨ HOPE IT HELP U✨