Question

The perimeter of right triangle is 40 cm and its hypotenuse measure 17 cm find the area of the triangle

Answer 1

Let the triangle is ABC and AB is the hypotenus...then AB= 17 ..If one of the side is BC=x and the other is AC=y, then
x+y=40-17......(1)
Again x²+y²=17²....(2)
from (2),
(x+y)²-2xy=17²
→(40_17)²-2xy=17²
→xy=120.......(3)
∆ABC=xy/2=60

Answer 2

Area = 60 cm²

Step-by-step explanation:

Given:

• Perimeter of right angled triangle is 40 cm.
• Measure of hypotenuse of triangle is 17 cm.

To Find:

• What is the area of triangle ?

Solution: Let in ∆ABC,

• Hypotenuse = AC = 17 cm
• Perpendicular = AB = x cm
• Base = BC = y cm
• Perimeter of ABC = 40 cm

As we know that Perimeter = Sum of all sides

40 = AB + BC + CA

40 = x + y + 17

40 – 17 = x + y

23 = x + y

(23 – y) = x.........(1)

Now according to Pythagoras thereom we know that Hypotenuse² = Base² + Perpendicular²

$\implies{\rm }$ 17² = y² + x²

$\implies{\rm }$ 289 = y² + (23 – y)²

$\implies{\rm }$ 289 = y² + 23² + y² – 2•23•y

$\implies{\rm }$ 289 = 2y² + 529 – 46y

$\implies{\rm }$ 0 = 2y² – 46y + 529 – 289

$\implies{\rm }$ 0 = 2y² – 46y + 240

$\implies{\rm }$ 0 = 2(y² – 23y + 120)

Break the equation by middle term splitting method.

y² – 23y + 120

y² – 15y – 8y + 120

y(y – 15) – 8(y – 15)

(y – 8) or (y – 15)

y = 8 or y = 15

Put the value of y = 8 in equation 1

23 – 8 = x

15 = x

Area of triangle = 1/2 × Base × Height

Area = 1/2 × 8 × 15

Area = 4 × 15 = 60 cm²

Hence, area of right triangle will be 60 cm².