Question

the perimeter of a right angle triangle is 60 cm and its hypotenuse is 25 cm. Find the area of the triangle. Plsss help to solve this question.........​

Answer 1

$\huge\underline\mathrm{AnswEr:-}$

Area of triangle = 150 cm²

$\huge\underline\mathrm{GivEn:-}$

• Hypotenuse = 25 cm
• Perimeter of triangle = 60 cm

$\huge\underline\mathrm{To\:Find:-}$

Find the area of triangle = ?

$\huge\underline\mathrm{SoLution:-}$

Let ABC be a right angle triangle, since the perimeter of right angle triangle = 60 cm

Thus,

$\implies$$\mathrm{AB + BC + CA = 60 }$

$\implies$$\mathrm{AB + BC + 25 = 60}$

$\implies$$\mathrm{ AB + BC = 60 - 25 }$

$\large\bf{AB + BC = 35 ...1)}$

Squaring on both sides in equation 1)

$\implies$(AB + BC)² = (35)²

$\implies$AB² + BC² + 2(AB)(BC) = (35)²

$\implies$2(AB)(BC) = (35)² -(AB² + BC²)

$\implies$2(AB)(BC) = (35)² -(25)² ....[ ∴By Pythagoras theorem, AB² + BC² = 25]

$\implies$$\mathrm{ <strong>2(AB)(BC) = 1225 - 625</strong><strong> </strong>}$

$\implies$$\mathrm{ 2(AB)(BC) = 600}$

$\implies$$\mathrm{ (AB)(BC) =}$ $\large{\rm {\frac{600}{2}}}$

$\implies$$\bf{(AB)(BC) = 300}$

Since, the area of triangle = $\large{\sf {\frac{1}{2}}}$ base$\times$ height

$\implies$ $\large{\sf {\frac{1}{2}}}$ $\times$300[∴(AB)(BC) = 300... Find above]

$\implies$ 150 cm²

Area of triangle = 150 cm²

Answer 2

Answer:

$\implies$ Area of triangle = 150cm²

$\large\underline\mathrm{Given:-}$

• Hypothenuse = 25cm
• Perimeter of triangle = 60cm

$\large\underline\mathrm{To \: find}$

• The area of triangle = ?

$\large\underline\mathrm{Solution}$

• Let's ABC be a right angle triangle since the perimeter of right angle triangle = 60cm.

Thus,

$\implies$ AB + BC + CA = 60

$\implies$ AB + BC + 25 = 60

$\implies$ AB + BC = 60 - 25

$\implies$ AB + BC = 35..(1)

Squaring on both side in equation (1).

$\implies$ (AB + BC)² = (35)²

$\implies$ AB² + BC² + 2(AB)(BC) = (35)²

$\implies$ 2(AB)(BC) = (35)² - (25)²

[by Pythagoras theorem AB² + BC² = 25]

$\implies$ 2(AB)(BC) = 1215 - 625

$\implies$ 2(AB)(BC) = 600

$\implies$ (AB)(BC) = 600/2

$\implies$ (AB)(BC) = 300

Hence,

The area of triangle = 1/2 base × height.

$\implies$ 1/2 × 300 [(AB)(BC) = 300]

$\implies$ 150

$\implies$ Area of triangle = 150cm²