Question

if the perimeter of a right triangle is 60 cm qnd its hypotensuse is 25cm ,find its area​

Answer 1

Answer:

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Answer 2

Given:-

• Perimeter if Right triangle = 60cm

• Hypotenuse = 25cm

To Find:-

• Area of Triangle.

Construction.

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Here,

AB = 25cm.

FORMULAE USED:-

• (Base)² + (Height)² = (Hypotenuse)²

• Area of Triangle = ½ × Base × Height.

Now,

→ Perimeter of triangle = 60cm

→ AB + BC + AC = 60cm

→ BC + AC = 60 - 25

→ BC + AC = 35

→ BC = 35 - AC.

Let, AC = x, BC = 35 - x

Therefore,

→ (Base)² + (Height)² = (Hypotenuse)²

→ (BC)² + (AC)² = (AB)²

→ (35 - AC)² + (AC)² = (25)²

→ 35² - 2 × 35 × AC + AC² + AC² = 625

→ 1225 - 70AC + AC² + AC² = 625

→ 1225 - 70x + 2x² = 625

→ -70x + 2x² = 625 - 1225

→ -70x + 2x² = 600

→ 2x² - 70x + 600 = 0

→ 2x - 40x - 30x + 600 = 0

→ 2x( x - 20) - 30(x - 20) = 0

→ 2x - 30 = 0 → 2x = 30 → x = 15.

→ x - 20 → x = 20

Now,

Here we find the "x".

→ Base = BC → 35 - x → 35 - 15 = 20cm

→ Height = AC → x → 15cm.

Now,

→ Area of triangle = ½ × Base × Height

→ Area of triangle = ½ × 20 × 15 → 150cm²

Hence, The Area of Triangle is 150cm²