Question

2 points
2. The base of a right triangle
is 8cm and hypotenuse is
10cm. Its area will be *
O 24 sq.cm
O O O
O 40 sq.cm
O 48 sq.cm
O
80 sq.cm​

Answer 1

★ ANSWER ★

• 24 cm² (✔)

GIVEN:

• Base of the right triangle = 8 cm
• Hypotenuse of right triangle = 10 cm

TO FIND:

• What is the area of the triangle ?

SOLUTION:

Let the perpendicular of the right triangle be 'p' cm

To find the perpendicular of the triangle, we use the Pythagoras theorem

$\large{\boxed{\bf{\star \: (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2 \: \star}}}$

• Hypotenuse = 10 cm
• Base = 8 cm
• Perpendicular = p cm

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow (10)^2 = (8)^2 + (p)^2 }$

$\rm{\dashrightarrow 100 = 64 + p^2}$

$\rm{\dashrightarrow 100 - 64 = p^2}$

$\rm{\dashrightarrow 36 = p^2 }$

$\rm{\dashrightarrow \sqrt{36} = p }$

$\bf{\dashrightarrow 6 \: cm = p }$

We know that the formula for finding the area of the triangle is:-

$\large{\boxed{\bf{\star \: AREA = \dfrac{1}{2} \times base \times height \: \star}}}$

• Base = 8 cm
• Height = 6 cm

On putting the given values in the formula, we get

$\rm{\dashrightarrow Area = \dfrac{1}{\cancel{2}} \times \cancel{8} \times 6 }$

$\rm{\dashrightarrow Area = 4 \times 6 }$

$\bf{\dashrightarrow AREA = 24 \: cm^2 }$

❝ Hence, the area of the triangle is 24 cm² ❞

______________________