Question

find the area of a right triangle with hypotenuse 50 cm and
altitude 40 cm.​

Answer 1

Given:

• The hypotenuse of a triangle is 50cm
• The attitude of the triangle is 40cm

To Find:

• The area of the triangle

Solution:

➤ Now as we have the measurements of the altitude and the hypotenuse of the triangle let's usse pythagoras therom to find the measurement of its base and then we can find the area of the triangle.

${ \underline{ \underline{ \red{ \rm{Pythagoras \: Therom : }}}}}$

$\: \: \: \: \: \dag \bigg[ \bf \: {(Hypotenuse)}^{2} = {(Side)}^{2} + {(Base)}^{2} \bigg]$

★ Applying Concept :

${ : \implies} \sf {(H)}^{2} = {(S)}^{2} + {(B)}^{2} \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf {(50m)}^{2} = {(40m)}^{2} + {(B)}^{2} \\ \\ \\ { : \implies} \sf 2500 {m}^{2} = 1600 {m}^{2} + {(B)}^{2} \\ \\ \\ { : \implies} \sf {(B)}^{2} = 2500 {m}^{2} - 1600 {m}^{2} \\ \\ \\ { : \implies} \sf {(B)}^{2} = 900 {m}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf B = \sqrt{900 {m}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf B = 30m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the base of the triangle is 30m

★ Now,

• Let's find the area of the triangle

★ We know,

$\: \: \: \: \: \dag \bigg[ \bf \: area _{(triangle} = \frac{1}{2} \times b \times h\bigg]$

★ Putting the values we get,

${ : \implies} \sf area = \frac{1}{2} \times base \times hiegth \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf area = \frac{1}{2} \times 30m \times 40m \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf area = 15m \times 40m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf area = 600 {m}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence:

• The area of the triangle is 600m²

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Answer 2

Given -

• Hypotenuse of a right triangle is 50cm and it's altitude is 40cm.

⠀

To find -

• Area of the right triangle.

⠀

Solution -

For finding the area of a right triangle, we should have to find the length of its base.

For finding base, we will use the Pythagoras theorem.

⠀

According to pythagoras theorem

★ Hypotenuse ² = Base ² + Height ²

⠀

→ (50)² = Base² + (40)²

→ 2500 = Base² + 1600

→ Base² = 2500 - 1600

→ Base² = 900

→ Base = √900

→ Base = 30

⠀

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Now, we have height and base of the triangle. We can easily calculate the area of the triangle.

⠀

★ Area of triangle = ½ × base × height

⠀

→ Area = ½ × 30 × 40

→ Area = 15 × 40

→ Area = 600 cm²

⠀

Hence,

• Area of the right triangle is 600 cm².

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